Data structures for adaptive grid generation
SIAM Journal on Scientific and Statistical Computing
Simple adaptive grids for 1-d initial value problems
Journal of Computational Physics
Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows
Journal of Computational Physics
The LASY preprocessor and its application to general multidimensional codes
Journal of Computational Physics
r-refinement for evolutionary PDEs with finite elements or finite differences
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Comparison of Different Computer Platforms for Running the Versatile Advection Code
HPCN Europe 1998 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Simulating Magnetised Plasma with the Versatile Advection Code
VECPAR '98 Selected Papers and Invited Talks from the Third International Conference on Vector and Parallel Processing
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In many plasma physical and astrophysical problems, both linear and nonlinear effects can lead to global dynamics that induce, or occur simultaneously with, local phenomena. For example, a magnetically confined plasma column can potentially posses global magnetohydrodynamic (MHD) eigenmodes with an oscillation frequency that matches a local eigenfrequency at some specific internal radius. The corresponding linear eigenfunctions then demonstrate large-scale perturbations together with fine-scale resonant behaviour. A well-known nonlinear effect is the steepening of waves into shocks where the discontinuities that then develop can be viewed as extreme cases of 'short wavelength' features. Numerical simulations of these types of physics problems can benefit greatly from dynamically controlled grid adaptation schemes. Here, we present a progress report on two different approaches that we envisage to evaluate against each other and use in multi-dimensional hydro- and magnetohydrodynamic computations. In r-refinement, the number of grid points stays fixed, but the grid 'moves' in response to persistent or developing steep gradients. First results on 1D and 2D MHD model problems are presented. In h-refinement, the resolution is raised locally without moving individual mesh points. We show 2D hydrodynamic 'shock tube' evolutions where hierarchically nested patches of subsequently finer grid spacing are created and destroyed when needed. This adaptive mesh refinement technique will be further implemented in the Versatile Advection Code, so that its functionality carries over to any set of near conservation laws in one, two, or three space dimensions.