"LOGOS-WAVE" ("LOGOS-VOLNA") METHOD TO COMPUTE 2D GAS-DYNAMIC PROBLEMS WITH ACCOUNT FOR THERMAL CONDUCTIVITY ON MOVING UNSTRUCTURED GRIDS
E. A. Veselova, Yu. N. Deryugin, D. K. Zelenskiy
VANT. Ser.: Mat. Mod. Fiz. Proc 2021. Вып.4. С. 50-66.
A method for parallel computations on 2D gas-dynamic problems with account for thermal conductivity on geometrically adaptive unstructured grids is described. Geometrical adaptation is related to identification of basic specific features in the solution such as shock waves and contact discontinuities. The motion velocity at discontinuities and parameters at discontinuities are found from solution of Riemann problem. Displacement of internal nodes of the mesh is determined with boundary-node-displacement interpolation method. The numerical method is based on split method, on the solution of Eulerian equations explicitly on moving mesh and on the solution of heat-conductivity equation implicitly on immobile mesh. Difference equations are produced with discretization of initial equations in integral form with quadrature formulas of rectangles. When solving Eulerian equations, numerical convective flows are found on the basis of Riemann problem solution. Pre-discontinuity parameters of the flow are found using either linear or quadratic reconstruction of the solution to improve simulation accuracy. Algorithm of additional turn of the velocity vector of pre-discontinuity parameters of the flow is used in problems with spherical symmetry to decrease nonmonotonic character of numerical solution. Heat flows at the facets are approximated by the upper time layer with central differences. Iteration Newton method is used to solve implicit equations. The system of linear algebraic equations resulted from approximation is solved using parallel solvers from PMLP library when temperature increment is regarded. Possibilities of the method are illustrated on a number of benchmarks. Keywords: gas dynamics, heat conductivity, splitting scheme, difference scheme, moving meshes, computation parallelization, testing computations.
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