IMPLICIT AND SEMIIMPLICIT SCHEMES IN THE VERSATILE ADVECTION CODE - NUMERICAL TESTS

We describe and evaluate various implicit and semiimplicit time integr ation schemes applied to the numerical simulation of hydrodynamical an d magnetohydrodynamical problems. The schemes were implemented recentl y in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with opt ional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computat ional cost is reduced. The test problems cover one and two dimensional , steady state and time accurate computations, and the solutions conta in discontinuities. For each test, we confront explicit with implicit solution strategies.