INTERACTION OF SOUND WITH MATERIAL-MATERIAL INTERFACE IN DIFFERENCE SCHEMES OF 1D LAGRANGIAN GAS DYNAMICS. ACCURACY DEPENDENCE ON THE GRID ADJUSTMENT METHOD
VANT. Ser.: Mat. Mod. Fiz. Proc 2015. Вып.2. С. 12-27.
In some difference schemes for 1D gas dynamics on Lagrangian grids (without account for artificial viscosities) the difference coefficients of sound perturbation reflection from the material-material interface have been calculated and the difference laws of acoustic energy preservation have been built. It is shown that in the difference schemes on scattered special grids (the "cross" scheme and the scheme with artificial antidispersion) the difference reflection coefficient matches the analytical one (obtained for the acoustics differential equations) only when the grid on the material-material interface is adjusted over the acoustic thickness. The difference coefficients of acoustic perturbation reflection in the KABARE and Godunov’s difference schemes always (independently of the way the grid is adjusted) match the analytical value, but other types of errors are indicated which are proportional to the jump of the cell acoustic thickness.
The calculation of the weak shock passage through a periodical stratified medium have shown that when the grids adjusted over the acoustic thickness are used, the simulation accuracy can be improved by several times, while the running time can be reduced by more than an order of magnitude compared with the simulations on the mass-even grid, provided that the preset accuracy is preserved. Keywords: weak perturbations, dispersion equations, acoustic reflection coefficients, difference law of acoustic energy preservation, uneven grids, rules of grid adjustment on the material-material boundaries.
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