NON-UNIFORM GRID EFFECTS ON SHOCK PARAMETERS IN LAGRANGIAN DIFFERENCE SCHEMES WITH ARTIFICIAL VISCOSITY. ID ASYMPTOTIC ANALYSIS

Yu. A. Bondarenko, O. A. Moskalev
VANT. Ser.: Mat. Mod. Fiz. Proc 2006. Вып.4. С. 58-65.

It is well known that in the calculation that use Lagrangian difference schemes with artificial viscosity using the non-uniform grid, the propagated shock wave is perturbed, here the errors in shock parameters are proportionate to the quantity . It is demonstrated that the effect is the property of differential gas dynamics equations with viscosity, inherited by difference schemes. Approximate solutions to describe the interaction of the steady-state shock structure with the viscosity factor gradient have been set up by the asymptotic method, assuming that the shock is propagating in a resting gas of constant density and pressure and that there are no perturbations catching up with the shock front. The variable viscosity factor is constant in time, and it is assumed to be small compared to the characteristic dimensions determined by the spatial derivatives of the viscosity factor. The dominant term perturbations of shock parameters are directly proportionate to viscosity factor gradient. The results of numerical tests using Lagrangian difference schemes with artificial viscosity agree with the asymptotic form obtained.

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