*Astronomy and Astrophysics, 332, 1159-1170*
Paper (PostScript).

# Implicit and semi-implicit schemes in the Versatile Advection Code

**G. Toth [1], R. Keppens [2], M. A. Botchev [3]
**
- Astronomical Institute, Utrecht University, P.O. Box 80000, 3508 TA Utrecht, The Netherlands
- FOM-Institute for Plasma-Physics Rijnhuizen, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands
- Mathematical Institute, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands

## Abstract

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