Degenerate Hopf bifurcation in multiparameter hudrodynamical problems

Abstract: The method for computing Liapunov-Schmidt expansions in the analysis of degenerate Hopf bifurcation for equations with quadrate nonlinearity in Hilbert space was proposed. This algorithm was applied to the study of the loss of stability and bifurcations of Couette-Poiseuille and Kolmogorov viscous fluid flows.Note: Research direction:Mathematical problems and theory of numerical method

Comparative analysis of approaches for modeling of gasdynamic flows on two-level adaptive grids

Abstract: Different approaches to the modeling of gas-dynamic flows on adaptive grids compares in the example of the Sedov’s problem. Smoothness indicators based on the B-splines, and on the basis of complex and real Daubechies wavelets are used as a criterion for mesh refinement.Note: Research direction:Mathematical modelling in actual problems of science and technic

Algorithm for Multilevel Mesh Adaptation with Waveled-Based Criteria for Gas Dynamic Problems

Abstract: Algorithm for multilevel 2D-3D mesh refinement is suggested. For solution smoothness evaluation we use sliding window method with the patterns of cross and shape. To capture areas with high gradients of grid functions we use wavelet decomposition on this local patterns. Results about Sedov, Liska tests (2D) and supersonic flows about cavity and blunted body (3D) are presented.Note: Research direction:Mathematical modelling in actual problems of science and technic

Algorithm of local mesh adaptation based on wavelet analysis with the use of free boundary method

Abstract: Multiple level Cartesian mesh adaptation based on wavelet analysis is used for numerical simulation of flow past a solid nondeformable body that can move either according to some law (forced movement) or under the action of the reaction forces from the gas (free movement) using free boundary method.Note: Research direction:Mathematical modelling in actual problems of science and technic