DIFFERENCE-SCHEMES ON COMPOSITE GRIDS FOR HYPERBOLIC-EQUATIONS

Two classes of unconditionally stable difference schemes (DS) on adaptive time grids are proposed for the systems of equations of acoustics and a viscous barotropic gas. Accuracy estimates are obtained in both the linear and the non-linear case. By using different steps with respect to the variable t inside the computing domains, it is possible to reduce considerably the amount of computing required for the mathematical modelling of problems with singularities. The results of the theoretical analysis are confirmed by calculations on the problem of a piston moving into a gas.