olegvasilyev



Personal Websites

Oleg Vasilyev

Prof. Vasilyev received his MSc degree in Applied Mathematics and Physics from Moscow Institute of Physics and Technology in 1991, the MSc and PhD degrees in Mechanical Engineering from the University of Notre Dame, in 1994 and 1996, respectively, and Doctor of Sciences degree in Computational Mathematics in 2021 from Keldysh Institute of Applied Mathematics of Russian Academy of Sciences. Prior to rejoining Skoltech in 2023, Prof. Vasilyev has worked as a leading research scientist at the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, a consultant for Huawei Russian Research Institute in the position of Chief Project Engineer for the Extended Reality research group, a Professor at the Center for Design, Manufacturing and Materials of the Skolkovo Institute of Science and Technology (2017-2018), a Professor in the Department of Mechanical Engineering at the University of Colorado (2002-2016), an Assistant Professor in the Department of Mechanical and Aerospace Engineering at the University of Missouri – Columbia (1998-2002) and a Research Fellow at the Center for Turbulence Research, Stanford University (1996-1998). In 2016 Prof. Vasilyev has founded a consulting company Adaptive Wavelet Technologies, LLC, through which he has provided consulting services to Space Exploration Technologies Corporation (SpaceX) prior to joining the Skolkovo Institute of Science and Technology in 2017.

Prof. Vasilyev conducts research in the general area of theoretical and computational fluid mechanics with the emphasis on the creation of novel adaptive approaches for modeling and simulation of complex multi-scale phenomena, development of low order “physics-capturing” models and robust computational methodologies with tight integration of the numerics and physics-based modeling, and applications of these novel approaches to challenging multi-scale/multi-physics fluid problems of engineering and scientific interest. Prof. Vasilyev research has been supported by grants from Russian Science Foundation, National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), Argonne National Laboratory (ANL), Los Alamos National Laboratory (LANL), Department of Energy (DOE), Office of Naval Research (ONR), Caterpillar Inc., and United Sates Industry Coalition (USIC), with awards exceeding $12M ($4M as PI). Prof. Vasilyev is the author and co-author of more than 100 peer-reviewed journal and conference publications. He has given more than 200 lectures at conferences at universities around the world. In recognition of his accomplishments Prof. Vasilyev has been elected the recipient of Fredric William Basel Research Award from Alexander Von Humboldt Foundation, Germany, which is granted to scientists and scholars, internationally renowned in their field. In 2012 Prof. Vasilyev received the honor of being elected a Fellow of the American Physical Society “for pioneering work on adaptive wavelet methods for Computational Fluid Dynamics, fundamental contributions to the advancement of Adaptive Large Eddy Simulation approach and explicit filtering in LES, and the development of volume penalization methods for compressible flows.” In 2015 Prof. Vasilyev received a privilege of being elected a Fellow of the American Society of Mechanical Engineers “for the continuous and systematic effort in the development of a unified modeling and computational multi-scale framework that can be used for efficient modeling and simulation of complex multi-scale phenomena.”

RESEARCH INTERESTS

  • Computational Fluid Dynamics
  • Wavelet Methods for Modeling and Simulation of Complex Multi-Scale Phenomena
  • Theoretical and Numerical Studies in Turbulence
  • Large Eddy Simulations of Turbulent Flows
  • Turbulence Modeling

CURRENT RESEARCH TOPICS

Parallel adaptive wavelet Environment for Multiscale Modeling (PawEMM++)

Today there are a number of problems in engineering and science, which share a single common computational challenge: the ability to solve and/or model accurately and efficiently a wide range of spatial and temporal scales. Numerical simulation of such problems requires either the use of highly adaptive physics based numerical algorithms, the use of reduced models that capture “important” physics of the problem at a lower cost, or the combination of both approaches. In addition, with the rapidly increasing ability to model large problems and the constant demand to extract and visualize the information relatively quickly or even interactively, the scientific visualization of very large data sets has become a challenge in itself. Currently we are working on development of multi-scale modeling and simulation environment capable of performing different fidelity simulations for single/multi-phase, inert/reactive, compressible/incompressible, transitional and turbulent flows in complex geometries. At the core of the problem solving environment is an integrated adaptive multi-scale/multi-form modeling and simulation framework that on-the-fly identifies regions of the flow with a suitable model-form, differentiates the most dominant (energetic) structures that control the overall dynamics of the flow; and resolves and “tracks” on a space-time adaptive mesh these dynamically-dominant flow structures, while modeling the effect of the unresolved motions using the compatible multi-level model form. The unique feature of the problem-solving environment is a unified, dynamically adaptive, wavelet multi-resolution (multi-scale), and multi-form approach to numerical algorithms and solvers, modeling and visualization.

Hierarchical Wavelet-based Modeling of Turbulent Flows

Since the inception of Computational Fluid Dynamics, turbulence modeling and numerical methods evolved as two separate fields of research with the perception that once a turbulence model is developed, any suitable computational approach can be used for the numerical simulations of the model. Latest advancements in wavelet-based adaptive multi-resolution methodologies for the solution of partial di erential equations, combined with the unique properties of wavelet analysis to unambiguously identify and isolate localized dynamically dominant flow structures, make it feasible to develop a cardinally different framework for hierarchical modeling and simulation of turbulent flows that fully utilizes spatial/temporal turbulent flow intermittency and tightly integrates numerics and physics-based modeling. The integration is achieved by combining spatially and temporally varying wavelet thresholding with hierarchical wavelet-based turbulence modeling. The resulting approach provides automatic smooth transition from directly resolving all flow physics to capturing only the energetic/coherent structures, leading to a dynamically adaptive variable fidelity approach.  Our current efforts are focused on the development of  the unified framework  that will allow for synergistic transition among models of different hierarchy, namely, the adaptive Wavelet-based DNS, the Adaptive wall-resolved LES, Adaptive wall-modeled LES, and adaptive wavelet-based Unsteady RANS and application of the approach to modeling and simulation of industrially relevant flows.

Parallel Adaptive Wavelet Collocation Method (P-AWCM) for Solution of Multi-Scale Problems

Four general classes of methods for solving nonlinear partial differential equations on adaptive computational meshes have been developed by our group. Each method uses the adaptive wavelet collocation method (AWCM) based on bi-orthogonal lifted interpolating wavelets to construct a computational grid adapted to the solution. The wavelet decomposition naturally provides a set of nested multi-scale grids adapted to the solution, and we take advantage of this property in developing our methods. In the first two methods we implement a traditional time marching scheme for parabolic and hyperbolic partial differential equations, but use AWCM to adapt the computational grid to the solution at each time step. When hyperbolic equations are solved an additional wavelet-based procedure for shock capturing is used. With this procedure the mesh is refined in the vicinity of the shock up to a-priori specified resolution and the shock is smoothed out using localized numerical viscosity. The third method simply uses the multi-scale wavelet decomposition as the basis for an adaptive multilevel method for nonlinear elliptic equations. Recently, we have begun to investigate a combination of the first three approaches to produce an adaptive simultaneous space–time method. In this case, both the space-time grid adapts locally to the solution, and the final solution is obtained simultaneously in the entire space–time domain of interest. Our current efforts are focused on further development of the parallel wavelet-based methods with mesh and anisotropy adaptation.

OPEN SOURCE SOFTWARE

Adaptive Wavelet Collocation Method (AWCM-1D)
Matlab and Python 1D Demos

AWCM-1D is an open sourced MATLAB and Python libraries for learning and demonstration of Adaptive Wavelet Collocation Method. It offers a collection of subroutines/algorithms essential for developing/undrstanding of the Adaptive Wavelet Collocation Method (AWCM). The technical details of the AWCM are described in the paper by Vasilyev and Bowman (J. Comp. Phys., 2000). All demo subroutines are written for clarity of understanding of the algorithm without any consideration for efficiency. The software is accessible on GitLab under MIT Open Source Licence and can be accessed via the follwoing link: https://gitlab.com/awcm-1d.

Invited, Feature, and Review Articles

  1. Vasilyev, O.V., Yuen, D.A., and Paolucci, S., The Solution of PDEs Using Wavelets. Computers in Phys., 11(5),pp. 429-435, 1997.
  2. Vasilyev, O.V., Solving Multi-Dimensional Evolution Problems with Localized Structures Using Second Generation Wavelets. Int. J. Comp. Fluid Dyn., Special issue on High-Resolution Methods in Computational Fluid Dynamics, 17(2), pp. 151-168, 2003.
  3. Schneider, K. and Vasilyev, O.V., Wavelet Methods in Computational Fluid Dynamics. Ann. Rev. Fluid
    Mech.
    , 42, pp. 473-503, 2010.
  4. De Stefano, G. and Vasilyev, O.V., Hierarchical Adaptive Eddy-Capturing Approach for Modeling and Simulation of Turbulent Flows. Fluids, 6(2), 83, https://doi.org/10.3390/fluids6020083, 2021.
  5. Ge, Х., De Stefano, G., Vasilyev, O.V., and Hussaini, M.Y., Wavelet-based Adaptive Eddy-Resolving Methods for Modeling and Simulation of Complex Wall-bounded Compressible Turbulent FlowsFluids. 6(9), 331, https://doi.org/10.3390/fluids6090331, 2021.

Articles in Refereed Journals

  1. Vasilyev, O.V., and Paolucci, S., Stability of Unstably Stratified Shear Flow in a Channel Under Non-Boussinesq Conditions. ACTA Mechanica, 112, pp. 37-58, 1995.
  2. Vasilyev, O.V., and Paolucci, S., and Sen, M., A Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain. J. Comp. Phys. 120, pp.33-47, 1995.
  3. Vasilyev, O.V., and Paolucci, S., A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain. J. Comp. Phys., 125, pp. 498-512, 1996.
  4. Vasilyev, O.V., and Paolucci, S., A Fast Adaptive Wavelet Collocation Algorithm for Multi-Dimensional PDEsJ. Comp. Phys., 138, pp. 16-56, 1997.
  5. Vasilyev, O.V., Yuen, D.A., and Podladchikov, Yu.Yu.,  Applicability of Wavelet Algorithm for Geophysical Viscoelastic Flow.
    Geophys. Res. Lett.
    , 24(23), pp. 3097-3100, 1997.
  6. Morinishi, Y., Lund, T.S., Vasilyev, O.V., and Moin, P., Fully Conservative Higher Order Finite Difference Schemes for Incompressible FlowJ. Comp. Phys., 143, pp. 90-124, 1998.
  7. Vasilyev, O.V., Podladchikov, Yu.Yu., and Yuen, D.A.,  Modeling of Compaction Driven Flow in Poro-Viscoelastic Medium Using Adaptive Wavelet Collocation Method. Geophys. Res. Lett., 25(17), pp. 3239-3242, 1998.
  8. Vasilyev, O.V., Lund, T.S., and Moin, P., A General Class of Commutative Filters for LES in Complex Geometries. J. Comp. Phys., 146, pp. 105-123, 1998.
  9. Vasilyev, O.V., High Order Finite Difference Schemes on Non-Uniform Meshes with Good Conservation PropertiesJ. Comp. Phys., 157, pp. 746-761, 2000.
  10. Kardashov, V.R., Eppelbaum, L.V., and Vasilyev, O.V., The Role of Nonlinear Source Terms in Geophysics. Geophys. Res. Lett., 27(14), pp. 2069-2072, 2000.
  11. Vasilyev, O.V. and Bowman, C., Second Generation Wavelet Collocation Method for the Solution of Partial Differential Equations. J. Comp. Phys., 165, pp. 660-693, 2000.
  12. Winckelmans, G.S., Wray, A.A., Vasilyev, O.V., and Jeanmart, H., Explicit-Filtering Large-Eddy Simulation Using the Tensor-Diffusivity Model Supplemented by a Dynamic Smagorinsky TermPhys. Fluids, 13(5), pp. 1385-1403, 2001.
  13. Morinishi, Y. and Vasilyev, O.V., A Recommended Modification to the Dynamic Two-parameter Mixed Subgrid Scale Model for Large Eddy Simulation of Turbulent FlowPhys. Fluids, 13(11), pp. 3400-3410, 2001.
  14. Vasilyev, O.V., Podladchikov, Yu.Yu., and Yuen, D.A., Modeling of Viscoelastic Plume-Lithosphere Interaction Using Adaptive Multilevel Wavelet Collocation Method. Geophys. J. Int., 147(3), pp. 579-589, 2001.
  15. Vasilyev, O.V., Ten, A. A., and Yuen, D.A., Temperature-Dependent Viscous Gravity Currents with Shear
    Heating
    Phys. Fluids, 13(12), pp. 3664-3674, 2001.
  16. De Stefano, G. and Vasilyev, O.V., Sharp Cut-Off vs. Smooth Filtering in LESPhysics of Fluids, 14(1), pp. 362-369, 2002.
  17. Marsden, A.L., Vasilyev, O.V., and Moin, P. Construction of Commutative Filters for LES on Unstructured Meshes. J. Comp. Phys.175, pp. 584-603, 2002.
  18. Morinishi, Y. and Vasilyev, O.V., Vector Level Identity for Dynamic Subgrid Scale Modeling in Large Eddy Simulation. Physics of Fluids, 14(10), pp. 3616-3623, 2002.
  19. Vasilyev, O.V. and Kevlahan, N.K.-R., Hybrid Wavelet Collocation – Brinkman Penalization Method for Complex Geometry FlowsInt. J. Numer. Meth. in Fluids, 40, pp. 531-538, 2002.
  20. Haselbacher, A. and Vasilyev, O.V., Commutative Discrete Filtering on Unstructured Grids Based on Least-Squares Techniques. J. Comp. Physics, 187(1), pp. 197-211, 2003.
  21. Vasilyev, O.V. and Goldstein, D.E., Local Spectrum of Commutation Error in Large Eddy Simulations. Physics of Fluids, 16(2), pp. 470-473, 2004.
  22. Goldstein, D.E. and Vasilyev, O.V., Stochastic Coherent Adaptive Large Eddy Simulation MethodPhysics of Fluids, 16(7), pp. 2497-2513, 2004.
  23. Morinishi, Y., Vasilyev, O.V., and Ogi, T., Fully Conservative Finite Difference Scheme in Cylindrical Coordinates for Incompressible Flow Simulations. Journal of Computational Physics, 197(2), pp. 686-710, 2004.
  24. Vasilyev, O.V., Gerya, T.V, and Yuen, D.A., The Application of Multidimensional Wavelets to Unveiling Multi-Phase Diagrams and in Situ Physical Properties of Rocks. Earth and Planetary Science Letters, 223(1-2), pp. 49-64, 2004.
  25. Yuen, D.A., Erlebacher, G., Vasilyev, O.V., Goldstein, D.E., and Fuentes, M., Role of Wavelets in the Physical and Statistical
    Modeling of Complex Geological Processes
    Pure and Applied Geophysics, 161, pp. 2231-2244, 2004.
  26. De Stefano, G. and Vasilyev, O.V., Perfect Modeling Framework for Dynamic SGS Model Testing in Large Eddy SimulationTheoretical and Computational Fluid Dynamics18(1), pp., 27-41, 2004.
  27. Kevlahan, N.K.-R. and Vasilyev, O.V., An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction, SIAM Journal on Scientific Computing26(6), pp. 1894-1915, 2005.
  28. De Stefano, G., Goldstein, D.E., and Vasilyev, O.V., On the Role of Sub-grid Scale Coherent Modes in Large Eddy Simulation. Journal of Fluid Mechanics, 525, pp. 263-274, 2005.
  29. Vasilyev, O.V. and Kevlahan, N.K.-R., An Adaptive Multilevel Wavelet Collocation Method for Elliptic Problems. Journal of Computational Physics, 206(2), pp. 412-431, 2005.
  30. De Stefano, G., Vasilyev, O.V., and Goldstein, D.E., A-priori dynamic test for deterministic/stochastic modeling in large-eddy simulation of turbulent flow, Computer Physics Communications, 169, pp. 210-213, 2005.
  31. Goldstein, D.E., Vasilyev, O.V., and Kevlahan, N.K.-R., CVS and SCALES simulation of 3D isotropic turbulence, Journal of Turbulence, 6(37), pp. 1-20, 2005.
  32. Alam, J.M., Kevlahan, N.K.-R., and Vasilyev, O.V., Simultaneous space–time adaptive wavelet solution of nonlinear partial differential equations, Journal of Computational Physics214(2), pp. 829-857, 2006.
  33. Kevlahan, N.K.-R., Alam, J.M., and Vasilyev, O.V., Scaling of space-time modes with Reynolds number in two-dimensional turbulenceJournal of Fluid Mechanics, 570, pp. 217-226, 2007.
  34. Liu, Q. and Vasilyev, O.V.,  Brinkman Penalization Method for Compressible Flows in Complex GeometriesJournal of Computational Physics227(2), pp. 946-966, 2007.
  35. Vasilyev, O.V., De Stefano, G., Goldstein, D.E., and Kevlahan, N.K.-R., Lagrangian dynamic SGS model for SCALES of isotropic turbulenceJournal of Turbulence9(11), pp. 1-14, 2008.
  36. De Stefano, G., Vasilyev, O.V., and Goldstein, D.E., Localized Dynamic Kinetic Energy-based Models for Stochastic Coherent Adaptive Large Eddy Simulation, Physics of Fluids, 20(4), pp. 045102.1-045102.14, 2008.
  37. Regele, J.D. and Vasilyev, O.V., An Adaptive Wavelet-Collocation Method for Shock ComputationsInternational Journal of Computational Fluid Dynamics, 23(7), pp. 503-518, 2009.
  38. Ma, J., Hussaini, M.Y., Vasilyev, O.V., and Le Dimet, F.-X., Multiscale Geometric Analysis of Turbulence by CurveletsPhysics of Fluids, 21(7), pp. 075104.1-075104.19, 2009.
  39. Fujinoki, K. and Vasilyev, O.V., Triangular Wavelets: An Isotropic Image Representation with Hexagonal SymmetryEURASIP Journal on Image and Video Processing, Vol. 2009, Article ID 248581, 16 pages, 2009.
  40. Liu, Q. and Vasilyev, O.V., Nonreflecting Boundary Conditions Based on Nonlinear Multidimensional CharacteristicsInt. J. Num. Meth. Fluids62(1), pp. 24-55, 2010.
  41. De Stefano, G. andVasilyev, O.V., Stochastic coherent adaptive large eddy simulation of forced isotropic turbulenceJournal of Fluid Mechanics646, pp. 453-470, 2010.
  42. Reckinger, S.J., Livescu, D., and Vasilyev, O.V., Adaptive wavelet collocation method simulations of Rayleigh-Taylor instabilityPhysica Scripta, T142, 014064 (6pp), 2010.
  43. Gazzola, M., Vasilyev, O.V., and Koumoutsakos, P., Shape optimization for drag reduction in linked bodies using evolution strategiesComputers and Structures89, pp. 1224-1231, 2011.
  44. Regele, J.D., Kassoy, D.R., and Vasilyev, O.V., Effects of High Activation Energies on Acoustic Timescale Detonation InitiationCombustion Theory and Modelling, 16(4), pp. 650-678, 2012.
  45. De Stefano, G. and Vasilyev, O.V., A Fully Adaptive Wavelet-Based Approach to Homogeneous Turbulence Simulation,
    Journal of Fluid Mechanics695, pp. 149-172, 2012.
  46. Alam, J.M., Kevlahan, N.K.-R., and Vasilyev, O.V., A Multiresolution Model for the Simulation of Transient Heat and Mass Transfer, Numerical Heat Transfer, Part B, 61(3), pp. 147-170, 2012.
  47. Reckinger, S.M., Vasilyev, O.V., and Fox-Kemper, B., Adaptive Volume Penalization for Ocean ModelingOcean Dynamics, 62(8), pp. 1201-1215, 2012.
  48. Geers, T.L., Lagumbay, R.S., and Vasilyev, O.V., Acoustic-wave Effects in Violent Bubble Collapse,
    Journal of Applied Physics112(5), 054910, 2012.
  49. De Stefano, G. and Vasilyev, O.V., Wavelet-based adaptive large-eddy simulation with explicit filtering,
    Journal of Computational Physics, 238, pp. 240-254, 2013.
  50. Regele, J.D., Kassoy, D.R., Vezolainen, A., and Vasilyev, O.V., Indirect detonation initiation using acoustic timescale thermal power depositiongPhysics of Fluids, 25, 091113,doi:10.1063/1.4820130, 2013.
  51. Nejadmalayeri, A., Vezolainen, A., and Vasilyev, O.V., Reynolds Number Scaling of CVS and SCALESPhysics of Fluids, 25, 110823, doi:10.1063/1.4825260, 2013.
  52. Brown-Dymkoski, E., Kasimov, N., and Vasilyev, O.V., A Characteristic Based Volume Penalization Method for General Evolution Problems Applied to Compressible Viscous FlowsJournal of Computational Physics262, pp. 344-357, 2014.
  53. Reckinger, S.M., Vasilyev, O.V., and Fox-Kemper, B, Adaptive wavelet collocation method on the shallow water model,
    Journal of Computational Physics271, pp. 342-359, 2014.
  54. De Stefano, G. and Vasilyev, O.V., Wavelet-Based Adaptive Simulations of Three-Dimensional Flow Past a Square Cylinder,
    Journal of Fluid Mechanics748, pp. 433-456, 2014.
  55. Nejadmalayeri, A., Vezolainen, A., De Stefano, G., and Vasilyev, O.V., Fully adaptive turbulence simulations based on Lagrangian spatio-temporally varying wavelet thresholdingJournal of Fluid Mechanics749, pp. 794-817, 2014.
  56. Nejadmalayeri, A., Vezolainen, A., Brown-Dymkoski, E., and Vasilyev, O.V., Parallel Adaptive Wavelet Collocation Method for PDEsJournal of Computational Physics298, pp. 237-253, 2015.
  57. Souopgui, I., Scott A. Wieland, Hussaini, M.Y., and Vasilyev, O.V., Space-Time Adaptive Approach to Variational Data Assimilation Using WaveletsJournal of Computational Physics306, pp. 253-268, 2016.
  58. De Stefano, G., Nejadmalayeri, A., and Vasilyev, O.V., Wall-Resolved Wavelet-Based Adaptive Large-Eddy Simulation of Bluff-Body Flows with Variable ThresholdingJournal of Fluid Mechanics788, pp. 303-336, 2016.
  59. Reckinger, S.J., Livescu, D., and Vasilyev, O.V., Comprehensive Numerical Methodology for Direct Numerical Simulations of Compressible Rayleigh-Taylor InstabilityJournal of Computational Physics313, pp. 181-208, 2016.
  60. Regele, J.D., Kassoy, D.R., Aslani, M., and Vasilyev, O.V. Evolution of Detonation Formation Initiated by a Spatially Distributed, Transient Energy SourceJournal of Fluid Mechanics802, pp. 305-332, 2016.
  61. Brown-Dymkoski, E. and Vasilyev, O.V., Adaptive-Anisotropic Wavelet Collocation Method on General Curvilinear Coordinate SystemsJournal of Computational Physics333, pp. 414-426, 2017.
  62. De Stefano, G., Vasilyev, O.V., and Brown-Dymkoski, E., Wavelet-based adaptive unsteady RANS modeling of external flowsJournal of Fluid Mechanics837, pp. 765-787, 2018.
  63. Shervani-Tabar, N. and Vasilyev, O.V., Stabilized Conservative Level Set MethodJournal of Computational Physics375, pp. 1033-1044, 2018.
  64. Ge, X., Vasilyev, O.V., and Hussaini, M.Y., Wavelet-based adaptive delayed detached eddy simulations for wall-bounded compressible turbulent flowsJournal of Fluid Mechanics873, pp. 1116-1157, 2019.
  65. Ge, X., Vasilyev, O.V., De Stefano, G., and Hussaini, M.Y., Wavelet-Based Adaptive Unsteady Reynolds-Averaged Navier-Stokes Simulations of Wall-Bounded Compressible Turbulent Flows, AIAA Journal, 58(4), pp. 1529-1549, 2020.
  66. De Stefano, G., Brown-Dymkoski, E., and Vasilyev, O.V., Wavelet-based adaptive large-eddy simulation of supersonic channel flow, Journal of Fluid Mechanics901, A13, 2020.
  67. Abalakin, I.V., Vasilyev, O.V., Zhdanova, N.S., and Kozubskaya, T.K., Characteristic Based Volume Penalization Method for Numerical Simulation of Compressible Flows on Unstructured MeshesComputational Mathematics and Mathematical Physics. 61(8), pp. 1315–1329, https://doi.org/10.1134/S0965542521080029, 2021.
  68. Kasimov, N., Dymkoski, E., De Stefano, G., and Vasilyev, O.V., Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries. Fluids. 6(8), 293,  https://doi.org/10.3390/fluids6080293, 2021.
  69. Ge, X., Vasilyev, O.V., and Hussaini, M.Y., Wavelet-based adaptive wall-modeled large eddy simulation method for compressible turbulent flowsPhys. Rev. Fluids. 6(9), 094606,  https://doi.org/10.1103/PhysRevFluids.6.094606, 2021.
  70. Zhdanova, N.S., Abalakin, I.V., and Vasilyev, O.V., Generalized Brinkman volume penalization method for compressible flows around moving obstaclesMatem. Mod.. 34(2), pp. 41-57, 2022.
  71. De Stefano, G., Dymkoski, E., and Vasilyev, O.V., Localized dynamic kinetic-energy model for compressible wavelet-based adaptive large-eddy simulationPhys. Rev. Fluids. 7(5), 054604,  https://doi.org/10.1103/PhysRevFluids.7.054604, 2022.
  72. Mishin, Yu.A., Vasilyev, O.V., and Gerya, T.V., A wavelet-based adaptive finite element method for the Stokes problems. Fluids7(7), 221,   https://doi.org/10.3390/fluids7070221, 2022.
  73. Vezolainen, A.V., Erlebacher, G., Vasilyev, O.V., and Yuen, D.A., Volumetric rendering on wavelet-based adaptive grid. Fluids. 7(7), 245,   https://doi.org/10.3390/fluids7070245, 2022.
  74. Mehta, Y., Goetsch, R., Vasilyev, O.V., and Regele, J.D., A particle resolved simulation approach for studying shock interactions with moving, colliding solid particlesComputers and Fluids248, 105670,  https://doi.org/10.1016/j.compfluid.2022.105670, 2022.
  75. Zhdanova, N. S. and Vasilyev, O. V.,Penalized Wall Function Method for Turbulent Flow ModelingSupercomputing Frontiers and Innovations. 7(7), pp. 55-68, https://doi.org/10.14529/jsfi220406, 2022.
  76. Vasilyev, O.V. and Zhdanova, N.S.,Characteristic-Based Volume Penalization-Imposed Wall Function Method for Turbulent Boundary Layer ModelingComputational Mathematics and Mathematical Physics. 63(5), pp. 821–836, https://doi.org/10.1134/S0965542523050160, 2023.
  77. Vasilyev, O.V. and Zhdanova, N.S.,Generalization of the Penalized Wall Function Method for Modeling of Turbulent Flows with Adverse Pressure GradientComputational Mathematics and Mathematical Physics. 63(12), pp. 2384–2401, https://doi.org/10.1134/S0965542523120199, 2023.

Invited Conference and Symposium Papers

  1. Vasilyev, O.V., Computational Constrains on Large Eddy Simulation of Inhomogeneous Turbulent Complex Geometry Flows.  In Proceedings of Third AFOSR International Conference on DNS/LES, Edited by C. Liu et al., Greyden Press, Columbus, pp. 93-104, 2001.
  2. Vasilyev, O.V., Nejadmalayeri, A., De Stefano, G., Continuously Variable Fidelity Adaptive Large Eddy Simulation.  In Proceedings of Third International Workshop Computational Experiment in Aeroacoustics, Svetlogorsk, Russia, pp. 47-55, 2014.

Conference and Symposium Papers

  1. Paolucci, S., Suslov S.A., and Vasilyev, O.V., Stability of Mixed Convection Flow in a Differentially Heated Vertical Channel with Large Temperature Differences. In Fundamentals of Mixed Convection HTD-274, pp. 33-40, Edited by Chu, T.Y. and Chen, T.S., ASME, New York, 1994.
  2. Vasilyev, O.V., and Paolucci, S., Thermoacoustic Wave Propagation Modeling Using a Dynamically Adaptive Wavelet Collocation Method. In Proceedings of the ASME Heat Transfer Division, HTD-335, Volume 4, pp. 47-54, Edited by D.W. Pepper et al., ASME, 1996.
  3. Kevlahan, N.K.-R., Vasilyev, O.V., and Cherhabili, A., An Adaptive Wavelet Method for Turbulence in Complex Geometries. In Proceedings of the 16th IMACS World Congress 2000, 411-39.pdf, Edited by M. Deville and R. Owens, IMACS, 2000.
  4. Vasilyev, O.V. and Kevlahan, N.K.-R.,  Hybrid Wavelet Collocation – Brinkman Penalization Method for Complex Geometry Flows. In M.J. Baines, editor, Numerical Methods for Fluid Dynamics VII, ICFD, Oxford, University Computing Laboratory, pp. 509-515, 2001.
  5. Kevlahan, N.K.-R. and Vasilyev, O.V. An adaptive wavelet method for fluid-structure interaction. In Direct and Large-Eddy Simulation Workshop 4: University of Twente, ed. B. J. Geurts, R. Friedrich and O. Metais, pp. 253-260, 2001.
  6. De Stefano, G. and Vasilyev, O.V., A study of the effect of smooth filtering in LES. In Proceedings of Third AFOSR International Conference on DNS/LES, Edited by C. Liu et al., Greyden Press, Columbus, pp. 247-254, 2001.
  7. Kevlahan, N.K.-R.,Vasilyev, O.V., Goldstein, D.E., and Jay, A., A three-dimensional adaptive wavelet method for fluid-structure interaction. In Proceedings of Direct and Large-Eddy Simulation Workshop 5, Technical University of Munich, Germany, 2003.
  8. Goldstein, D.E., Vasilyev, O.V., and Kevlahan, N.K.-R., Feasibility Study of an Adaptive Large Eddy Simulation Method. AIAA Paper 2003-3551, 2003.
  9. De Stefano, G., Vasilyev, O.V., Goldstein, D.E., A-priori dynamic test for deterministic/stochastic modelling in LES of turbulent flow, In Proceedings of Conference on Computational Physics, Genoa, Italy, 2004.
  10. Lagumbay, R.S., Vasilyev, O.V., Haselbacher, A., and Wang, J., Numerical Simulation of a High Pressure Supersonic Multiphase Jet Flow Through a Gaseous Media, In Proceedings of the 16th International Mechanical Engineering Congress and Exposition, ASME, vol. 3, IMECE2004-61008, 2004.
  11. De Stefano, G., Vasilyev, O.V., Goldstein, D.E., and Kevlahan, N.K.-R., Towards Lagrangian dynamic SGS model for SCALES of isotropic turbulence, In Direct and Large-Eddy Simulation Workshop VI, Proceedings of the sixth international ERCOFTAC workshop on direct and large-eddy simulations, pp. 175-182, Edts. E. Lamballais, R. Friedrich, B. J. Geurts, and O. Metais, Springer, 2006.
  12. Lagumbay, R.S., Vasilyev, O.V., Haselbacher, A., and Wang, J., Numerical Simulation of a Supersonic Three-Phase Cavitating Jet Flow Through a Gaseous Medium in Injection Nozzle, In Proceedings of 2005 ASME International Mechanical Engineering Congress and Exposition, ASME, IMECE2005-82948, 2005.
  13. Liu, Q. and Vasilyev, O.V., Hybrid Adaptive Wavelet Collocation-Brinkman Penalization Method for DNS and URANS Simulations of Compressible Flow around Bluff Bodies, AIAA Paper 2006-3206, 2006.
  14. Sakakibara, S. and  Vasilyev, O.V., Image Processing with Triangular Biorthogonal Wavelets. In Proceedings of 14th European Signal Processing Conference, Florence, Italy, 2006.
  15. Kassoy, D., Regele, J.D. and Vasilyev, O.V., Detonation Initiation on the Microsecond Time Scale: Comparative One and Two Dimensional DDT Results Obtained from Adaptive Wavelet-Collocation Numerical Methods, AIAA Paper 2007-986, 2007.
  16. Regele, J.D., Kassoy, D., and Vasilyev, O.V., Numerical Modeling of Acoustic Timescale Detonation Initiation, AIAA Paper 2008-1037, 2008.
  17. De Stefano, G. and Vasilyev, O.V, Stochastic Coherent Adaptive Large-Eddy Simulation with Explicit Filtering, In Proceedings of the Workshop on Quality and Reliability of Large-Eddy Simulations II, Pisa, Italy, 2009.
  18. De Stefano, G. and Vasilyev, O.V, Stochastic Coherent Adaptive Large Eddy Simulation of Forced Isotropic Turbulence, In Direct and Large-Eddy Simulation VII, Proceedings of the Seventh International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 281-286, Edts. V. Armenio, B. Geurts, and J. Frohlich, Springer, 2010.
  19. Vasilyev, O.V. and De Stefano, G., Progress in the Development of Stochastic Coherent Adaptive LES Methodology, In Direct and Large-Eddy Simulation VII, Proceedings of the Seventh International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 303-307, Edts. V. Armenio, B. Geurts, and J. Frohlich, Springer, 2010.
  20. De Stefano, G. and Vasilyev, O.V., Towards Wavelet-based Adaptive Numerical Simulation of Turbulent Flow past Bluff-Bodies, In Proceedings of the 5th International Conference on Vortex Flow and Vortex Methods, Caserta, Italy, ISBN/ISSN: 978-88-905218-6-7, 2010.
  21. Nejadmalayeri, A., Vasilyev, O.V., Vezolainen, A., and De Stefano, G., Spatially Variable Thresholding for Stochastic Coherent Adaptive LES, In Direct and Large-Eddy Simulation VIII, Proceedings of the Eighth International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 95-100, Edts. H. Kuerten, B. Geurts, V. Armenio, and J. Frohlich, Springer, 2011.
  22. De Stefano, G. and Vasilyev, O.V., Stochastic Coherent Adaptive LES with Time-Dependent Thresholding, In Direct and Large-Eddy Simulation VIII, Proceedings of the Eighth International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 101-106, Edts. H. Kuerten, B. Geurts, V. Armenio, and J. Frohlich, Springer, 2011.
  23. Regele, J.D., Kassoy, D., and Vasilyev, O.V., Acoustic Timescale Detonation Initiation in 2-D and its Relationship with the 1-D Description, In: Proceedings of the 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine, CA 2011.
  24. Reckinger, S.J., Livescu, D., and Vasilyev, O.V. Simulations of Compressible Rayleigh-Taylor Instability Using the Adaptive Wavelet Collocation Method, In Proceedings of the Seventh International Conference on Computational Fluid Dynamics (ICCFD7), 2012.
  25. Regele, J.D., Kassoy, D., Vezolainen, A., and Vasilyev, O.V., Purely gasdynamic multidimensional indirect detonation initiation using localized acoustic timescale power deposition, AIAA-2013-1172, 2013.
  26. Regueiro, R., Pak, R., McCartney, J., Sture, S., Yan, B., Duan, Z., Svoboda, J., Mun, W., Vasilyev, O.V., Kasimov, N., Brown-Dymkoski, E., Hansen, C., Li, S., Ren, B., Alshibli, K., Druckrey, A., Lu, H., Luo, H., Brannon, R., Bonifasi-Lista, C., Yarahmadi, A., Ghodrati, E., Colovos, J., ONR MURI Project on Soil Blast Modeling and Simulation, In Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, pp. 341-353, 2014.
  27. De Stefano, G., Nejadmalayeri, A., and Vasilyev, O.V., Wavelet-based Computational Modeling of Wall-bounded Turbulent Flows with Lagrangian Variable Thresholding, In Proceedings of the Sixth European Conference on Computational Fluid Dynamics, 2014.
  28. Brown-Dymkoski, E., Kasimov, N., and Vasilyev, O.V, Characteristic-Based Volume Penalization Method for Arbitrary Mach Flows Around Solid Obstacles, In Direct and Large-Eddy Simulation IX, Proceedings of the Ninth International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 109-115, Edts. J. Frohlich, H. Kuerten, B.J. Geurts, and V. Armenio, Springer, 2015.
  29. De Stefano, G. and Vasilyev, O.V. DNS of Square-cylinder Flow using Hybrid Wavelet-Collocation/Volume-Penalization Method,In Direct and Large-Eddy Simulation IX, Proceedings of the Ninth International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 117-123, Edts. J. Frohlich, H. Kuerten, B.J. Geurts, and V. Armenio, Springer, 2015.
  30. Nejadmalayeri, A., Vasilyev, O.V, and Vezolainen, A., Computational Complexity of Adaptive LES with Variable Fidelity Model Refinement, In Direct and Large-Eddy Simulation IX, Proceedings of the Ninth International ERCOFTAC Workshop on Direct and Large-Eddy Simulations, pp. 149-153, Edts. J. Frohlich, H. Kuerten, B.J. Geurts, and V. Armenio, Springer, 2015.
  31. Dzwinel, W., Klusek, A., and Vasilyev, O., Supermodeling in simulation of melanoma progression, International Conference on Computational Science, Procedia Computer Science, 80, pp. 999-1010, 2016.
  32. De Stefano, G., Nejadmalayeri, A., and Vasilyev, O.V., Adaptive LES of Immersed-Body Flows Based on Variable Wavelet Threshold Filtering, In Direct and Large-Eddy Simulation X. ERCOFTAC Series, vol. 24, pp. 213-219, Edts. D. Grigoriadis, B. Geurts, H. Kuerten, J. Frohlich, V. Armenio, Springer, 2018.
  33. Ge, X., Vasilyev, O.V., De Stefano, G., and Hussaini, M.Y., Wavelet-based adaptive unsteady Reynolds-Averaged Navier-Stokes computations of wall-bounded internal and external compressible turbulent flows, AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, AIAA-2018-0545, doi.org/10.2514/6.2018-0545, 2018.
  34. Ge, X., Vasilyev, O.V., and Hussaini, M.Y., Wavelet-based delayed detached eddy simulation method for compressible wall bounded turbulent flow modeling, AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, AIAA-2018-0592, doi.org/10.2514/6.2018-0592, 2018.
  35. De Stefano, G., Brown-Dymkoski, E., and Vasilyev, O.V, Adaptive direct numerical simulation with spatially-anisotropic wavelet-based refinement, In Direct and Large-Eddy Simulation XI. ERCOFTAC Series, pp. 3-8, Edts. Salvetti, M.V., Armenio, V., Frohlich, J., Geurts, B.J., Kuerten, H., Springer, doi.org/10.1007/978-3-030-04915-7, 2019.
  36. Ge, X., Zhou, Y., Vasilyev, O.V., and Hussaini, M.Y., Adaptive Wavelet-based Delayed Detached Eddy Simulations of Anisothermal Channel Flows with High Transverse Temperature Gradients, AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, AIAA-2019-1558, doi.org/10.2514/6.2019-1558, 2019.
  37. Ge, X., Vasilyev, O.V., and Hussaini, M.Y., Adaptive Wavelet-based Delayed Detached Eddy Simulation of Shock Wave-Turbulent Boundary Layer Interaction in a Compression Ramp Flow, AIAA Aviation 2019 Forum,AIAA-2019-3704, doi.org/10.2514/6.2019-3704, 2019.
  38. De Stefano, G. and Vasilyev, O.V., Towards wavelet-based intelligent simulation of wall-bounded turbulent compressible flows, In Direct and Large-Eddy Simulation XII, DLES 2019. ERCOFTAC Series, vol. 27, pp. 285-290, Edts. Garcia-Villalba M., Kuerten H., Salvetti M., Springer, Cham, doi.org/10.1007/978-3-030-42822-8_37, 2020.
  39. Abalakin, I.V., Kozubskaya, T.K., Vasilyev, O.V., and Zhdanova, N.S., Characteristic-based volume penalization method for compressible flow simulations on unstructured meshes. In Proceedings of 14th WCCM-ECCOMAS Congress 2020, Edts.F. Chinesta, R. Abgrall, O. Allix and M. Kaliske, 2021.
  40. De Stefano, G. and Vasilyev, O.V., Wavelet-based Adaptive LES for Compressible Flows, In Direct and Large-Eddy Simulation XIII, DLES 2023. ERCOFTAC Series, vol. 31, pp. 197-202, Edts. Marchioli, C., Salvetti, M.V., Garcia-Villalba, M., Schlatter, P., Springer, Cham, doi.org/10.1007/978-3-031-47028-8_30, 2024.

Non-Refereed Articles

  1. Vasilyev, O.V. and Lund, T.S., A General Theory of Discrete Filtering for LES in Complex Geometry. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 67-82, 1997.
  2. Winckelmans, G.S., Wray, A.A., and Vasilyev, O.V., Testing of a new mixed model for LES: the Leonard model supplemented by a dynamic Smagorinsky term. In Proceedings of the 1998 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 367-388, 1998.
  3. Cottet, G.-H. and Vasilyev, O.V., Comparison of dynamic Smagorinsky and anisotropic subgrid-scale models. In Proceedings of the 1998 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 389-397, 1998.
  4. Vasilyev, O.V. and Bushe, W.K., On the use of a dynamically adaptive wavelet collocation algorithm in DNS of non-premixed turbulent combustion. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 65-81, 1998.
  5. Morinishi, Y.  and Vasilyev, O.V., Subgrid scale modeling taking the numerical error into consideration. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 237-253, 1998.
  6. Vasilyev, O.V., On the construction of high order finite difference schemes on non-uniform meshes with good conservation properties. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 311-324, 1998.
  7. Marsden, A.L. and Vasilyev, O.V., Commutative Filters for LES on Unstructured Meshes. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 382-402, 1999.
  8. Goldstein, D.A., Vasilyev, O.V., Wray, A.A., and Rogallo, R.S. Evaluation of The Use of Second Generation Wavelets in the Coherent Vortex Simulation ApproachIn Proceedings of the 2000 Summer Program, Center for Turbulence Research, NASA  Ames/Stanford Univ., pp. 293-304, 2000.
  9. Marsden, A.L., Vasilyev, O.V., and Moin, P. Construction of Commutative Filters for LES on Unstructured Meshes. In Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 169-182, 2000.
  10. Goldstein, D.E., Vasilyev, O.V., and Kevlahan, N.K.-R., Adaptive LES of 3D decaying isotropic turbulence, In Proceedings of the 2004 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 111-122, 2004.
  11. Moureau, V.R., Vasilyev, O.V., Angelberger, C. and Poinsot, T.J. Commutation errors in Large Eddy Simulation on moving grids, Application to piston engines flows, In Proceedings of the 2004 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 157-168, 2004.
  12. Vasilyev, O.V., Goldstein, D. E., De Stefano, G., Bodony, D., You, G., and Shunn, L., Assessment of local dynamic subgrid-scale models for Stochastic Coherent Adaptive Large Eddy Simulation, In Proceedings of the 2006 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 139-150, 2006.

ACADEMIC HONORS

  • Japan Society for Promotion of Science Invitation Fellowship for Research in Japan, Japan, 2016
  • Fellow of the American Society of Mechanical Engineers, USA, 2015
  • Mechanical Engineering Outstanding Graduate Educator Award, University of Colorado Boulder, USA, 2015
  • Fellow of the American Physical Society, Division of Fluid Dynamics, USA, 2012
  • Friedrich Wilhelm Bessel Research Award, Alexander Von Humboldt Foundation, Germany, 2008
  • Mechanical Engineering Outstanding Research Award, University of Colorado Boulder, USA, 2006
  • Mechanical Engineering Distinguished Achievement Award, University of Colorado, Boulder, USA, 2005
  • Faculty Early Career Development (CAREER) Award, National Science Foundation, USA, 2002
  • Center for Turbulence Research Postdoctoral Fellowship, Stanford University, USA, 1996-1998
  • Center of Applied Mathematics Fellowship, University of Notre Dame, USA, 1992-1994

Skolkovo Institute of Science and Technology (Skoltech) is pleased to announce a call for applications for PhD student and Research Scientist/Software Engineer/Postdoctoral  positions in the research group of Professor Oleg V. Vasilyev in the areas specified below:



2D Compressible Flow around Cylinder

Numerical simulations of compressible 2D flow around cylinder at Re=150 and Ma=0.2 using Adaptive Wavelet Collocation Method with charachterisrtic-based volume penalization.

W-DNS of Compressible Flow around Sphere, Re=1000, Ma=0.7

Wavelet-based Direct Numerical Simulation (W-DNS) of compressible flow around sphere, Re=1000, Ma=0.7: main vortical structures in the near wake identified by the iso-surfaces of iso-surfaces of the second invariant of the velocity gradient tensor for Q=0.25U2/D2 colored by the magnitude of vorticity.

W-DNS of Compressible Flow around Cylinder, Re=350, Ma=0.3

Wavelet-based Direct Numerical Simulation (W-DNS) of compressible flow around cylinder, Re=350, Ma=0.3: main vortical structures in the near wake identified by the iso-surfaces of iso-surfaces of the second invariant of the velocity gradient tensor forQ=0.1U2/D2 with corresponding computational mesh colored by the level of resolution.

W-DNS of Compressible Flow around Cylinder, Re=500, Ma=0.3

Wavelet-based Direct Numerical Simulation (W-DNS) of compressible flow around cylinder, Re=500, Ma=0.3: main vortical structures in the near wake identified by the iso-surfaces of iso-surfaces of the second invariant of the velocity gradient tensor forQ=0.5U2/D2.

2D Compressible Flow around Moving Cylinder

Numerical simulations of compressible 2D flow around moving cylinder using Adaptive Wavelet Collocation Method with charachterisrtic-based volume penalization.

Galilean Invariance for Characteristic-based Volume Penalization


Demonstration of Galilean invarience for inviscid supersonic flow around cylindrical particle using characteristic-based volume penalization with Adaptive Wavelet Collocation Method.

Shock Impinging on Array of Cylinders


Numerical simulations of shock impinging on array of cylinders using Adaptive Wavelet Collocation Method with charachterisrtic-based volume penalization.

Shock Impinging on а Wedge


Numerical simulations of shock impinging on а wedge using Adaptive Wavelet Collocation Method with charachterisrtic-based volume penalization.

Rayleigh-Taylor Instability

Numerical simulations of single-mode, compressible Rayleigh–Taylor instability using the Adaptive Wavelet Collocation Method.

Detonation Initiation


Numerical simulation of detonation initiation using acoustic timescale thermal power deposition with Adaptive Wavelet Collocation Method.

Particle-Fluid-Particle Interaction


Demonstration of particle-fluid-particle interaction for compressible flow using characteristic-based volume penalization with adaptive wavelet collocation method and soft-shell model for particle collision: density field with correspnding computational mesh colored by density and trasparent particle for demonstration of mesh adaptivity inside of the particles.

Профессор Васильев закончил Московский Физико-Технический Институт в 1991 г., получив степень магистра в области прикладной математики и физики. В 1994 и 1996 гг. профессор Васильев получил соответственно степени Магистра и Доктора Философии на факультете Аэрокосмической Техники и Механики Университета Нотр Дам, США. В 2021 году профессору Васильеву была присуждена ученая степень доктора физико-математических наук по специальности «вычислительная математика». До возвращения в Сколтех, профессор Васильев, работал ведущим научным сотрудником института прикладной математики им. Келдыша Российской академии наук, консультантом Российского исследовательского института Huawei в должности главного инженера проектов в исследовательской группе расширенной реальности, профессором Центра по проектированию, производственным технологиям и материалам Сколковского института науки и технологий (2017-2018 гг.), профессором факультета механики Университета Колорадо (2002-2016 гг.), доцентом факультета механики и аэрокосмической техники Университета Миссури – Колумбия (1998–2002 гг.) и научным сотрудником Центра исследований турбулентности Стэнфордского университета (1996–1998 гг.). В 2016 году профессор Васильев основал консалтинговую компанию ООО «Adaptive Wavelet Technologies», через которую он оказывал консультационные услуги Корпорации космических исследований (SpaceX) до прихода в Сколковский институт науки и технологий в 2017 году.

Профессор Васильев проводит исследования в областях вычислительной математики, теоретической и вычислительной механики жидкости и газа с акцентом на создание новых физико-разрешающих подходов численного моделирования, разрабатывает математические модели и адаптивные вычислительные методы, и применяет новые подходы к численному моделированию многомасштабных проблем жидкости и газа как научного так и прикладного характера. Его научные исследование были финансированы Российским научным фондом (РНФ), национальным научным фондом США (NSF), национальным управлением США по аэронавтике и исследованию космического пространства (NASA), департаментом энергетики США (DOE), национальной лабораторией Аргонн, США (ANL), национальной лабораторией Лос-Аламос, США (LANL), управление военно-морских исследований США (ONR), компанией Катерпиллер, США, и промышленной коалицией США (USIC) с общим объёмом финансирования превышающим $12 млн и $4 млн в качестве руководителя проекта. Профессор Васильев является автором и соавтором более 100 рецензируемых статей в журналах и материалах конференций. Профессор Васильев прочитал более 200 лекций на конференциях, в университетах и научных центрах по всему миру. В 2008 г., в знак признания его достижений, профессор Васильев был награждён Премией Фридриха Вильгельма Бесселя от фонда Александра фон Гумбольдта, Германия, которой награждаются ученые, всемирно известные в своей области. В 2012 г. профессор Васильев был избран Почётным Членом Американского Физического Общества за “новаторскую разработку адаптивных методов численного моделирования на основе вейвлетов, за фундаментальный вклад в развитие адаптивного метода крупных вихрей и подхода явной фильтрации в методе крупных вихрей, а также за развитие методов затопленных границ для сжимаемых течений.” В 2015 г. профессор Васильев был удостоен Почётного Членства Американского Общества Инженеров-Механиков за “непрерывные и систематические усилия в разработке обобщенного подхода численного моделирования многомасштабных явлений.”