Oleg V. Vasilyev

Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term

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 necessary LES truncations (grid and numerical method) are responsible for an additional subgrid-scale stress. A natural mixed model is then the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. This model is reviewed, together with useful connections to other models, and is tested against direct numerical simulation (DNS) of turbulent isotropic decay starting with Re-lambda=90 (thus moderate Reynolds number): LES started from a 256(3) DNS truncated to 64(3) and Gaussian filtered. The tensor-diffusivity part is first tested alone; the mixed model is tested next. Diagnostics include energy decay, enstrophy decay, and energy spectra. After an initial transient of the dynamic procedure (observed with all models), the mixed model is found to produce good results. However, despite expectations based on favorable a priori tests, the results are similar to those obtained when using the dynamic Smagorinsky model alone in LES without explicit filtering. Nevertheless, the dynamic mixed model appears as a good compromise between partial reconstruction of the filtered-scale stress and modeling of the truncations effects (incomplete reconstruction and subgrid-scale effects). More challenging 48(3) LES are also done: Again, the results of both approaches are found to be similar. The dynamic mixed model is also tested on the turbulent channel flow at Re-tau=395. The tensor-diffusivity part must be damped close to the wall in order to avoid instabilities. Diagnostics are mean profiles of velocity, stress, dissipation, and reconstructed Reynolds stresses. The velocity profile obtained using the damped dynamic mixed model is slightly better than that obtained using the dynamic Smagorinsky model without explicit filtering. The damping used so far is however crude, and this calls for further work

Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets

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 sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems.

An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers

Two mathematical approaches are combined to calculate high Rey\-nolds 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 the Poisson problem for the pressure at each time step. The method is applied to two-dimensional flow around fixed and moving cylinders for Reynolds numbers in the range

Stochastic Coherent Adaptive Large Eddy Simulation Method

3\times 10^1 \le Re \le 10^5

A recommended modification to the dynamic two-parameter mixed subgrid scale model for large eddy simulation of wall bounded turbulent flow

. The compression ratios of up to 1000 are achieved. For the first time it is demonstrated in actual dynamic simulations that the compression scales like

Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations

Re^{1/2}

Sharp cutoff versus smooth filtering in large eddy simulation

over five orders of magnitude, while computational complexity scales like

Modeling of compaction driven flow in poro-viscoelastic medium using adaptive wavelet collocation method

Re

Commutative discrete filtering on unstructured grids based on least-squares techniques

. This represents a significant improvement over the classical complexity estimate of

An adaptive wavelet-collocation method for shock computations

Re^{9/4}