We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional 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 computational cost is reduced.
The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.
Key words: methods: numerical - magnetohydrodynamics - hydrodynamics - shock waves