MULTIMESH APPROACH TO THE NUMERICAL SOLUTION OF GAS-DYNAMIC EQUATIONS BY CHARACTERISTIC DIRECTIONS METHOD WITH TRACKING STRONG AND WEAK DISCONTINUITIES FOR AN ARBITRARY EQUATION OF STATE

D. N. Bokov, N. N. Bokov
VANT. Ser.: Mat. Mod. Fiz. Proc 2000. Вып.2. С. 10-20.

A concept of a multimesh approach to solving gas-dynamic equations with the method of characteristic directions is presented in the paper. A determining system of difference equations for calculating continuous flow is written down in a form of linear combinations of finite increments of conservative variables along the characteristic directions for an arbitrary equation of state. Algorithms are given to calculate the main flow elements: centered rarefaction wave, interface, shock wave and decomposition of arbitrary discontinuity (Riemann problem). The multimesh approach enables development of tools for detailed description of the flow features based on hyperbolic system attributes and tracking interaction between all flow elements. Numerical calculations of the test problems, which prove the high accuracy reached at a small number of grid points are presented.