Oleg V. Vasilyev

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Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed(More)
An adaptive numerical method for solving partial differential equations is developed. The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O(N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for(More)
A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular(More)
A class of filters for large eddy simulations of turbulent inhomogeneous flows is presented. A general set of rules for constructing discrete filters in complex geometry is given and examples of such filters are presented. With these filters the commutation error between numerical differentiation and filtering can be made arbitrarily small, allowing for(More)
Liandrat and Tchiamichian [2], Bacry et al. [3], Maday and Ravel [4], and Bertoluzza et al. [5] have shown that A dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations. The the multiresolution structure of wavelet bases is a simple multilevel structure of the algorithm provides a simple(More)
Large-eddy simulation ~LES! with regular explicit filtering is investigated. The filtered-scale stress due to the explicit filtering is here partially reconstructed using the tensor-diffusivity model: It provides for backscatter along the stretching direction~s!, and for global dissipation, both also attributes of the exact filtered-scale stress. The(More)
This paper introduces the hybrid wavelet collocation Brinkman penalization method for solving the Navier–Stokes equations in arbitrarily complex geometries. The main advantages of the wavelet collocation method and penalization techniques are described, and a brief summary of their implementation is given. The hybrid method is then applied to a simple flow(More)
Dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time. These methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time. The same time step is used for all spatial locations and all scales: this(More)
Two mathematical approaches are combined to calculate high Reynolds number incompressible fluid-structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid boundaries of arbitrary complexity. We also implement a wavelet-based multilevel solver for(More)
Numerical simulation of turbulent flows (DNS or LES) requires numerical methods that are both stable and free of numerical dissipation. One way to achieve this is to enforce additional constraints, such as discrete conservation of mass, momentum, and kinetic energy. The objective of this work is to generalize the high order schemes of Morinishi et al. to(More)