## Implicit and semi-implicit schemes in the Versatile Advection Code: numerical tests
^{1} Astronomical Institute, Utrecht University, P.O. Box
80000, 3508 TA Utrecht, The Netherlands (toth@fys.ruu.nl)^{2} FOM-Institute for Plasma-Physics Rijnhuizen, P.O. Box
1207, 3430 BE Nieuwegein, The Netherlands (keppens@rijnh.nl)^{3} Mathematical Institute, Utrecht University, P.O. Box
80010, 3508 TA Utrecht, The Netherlands (botchev@math.ruu.nl)
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.
* Present address: Department of Atomic Physics, Eötvös Loránd University, Puskin u. 5-7, Budapest 1088, Hungary ## Contents- 1. Introduction
- 2. Numerical schemes
- 3. Equations
- 4. Model problems
- 4.1. Steady state accretion onto a black hole
- 4.1.1. Problem description and solution
- 4.1.2. Implicit versus explicit
- 4.2. Oscillating plasma sheet
- 4.2.1. Problem description and solution
- 4.2.2. Implicit versus explicit
- 4.3. Formation of a steady bow shock
- 4.3.1. Problem description and solution
- 4.3.2. Implicit versus explicit
- 4.4. MHD reconnection
- 4.4.1. Problem description and solution
- 4.4.2. Implicit versus explicit
- 4.1. Steady state accretion onto a black hole
- 5. Conclusions
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: March 30, 1998 |