VLUGR2: adaptive grid solver for PDEs in 2D
Developed in the
LUGR project, which until 1994 was part of
CWI's research program
Mathematics & the Environment.
Systems of (time-dependent) partial differential equations in two
space-dimensions having solutions with steep gradients in space and time.
The domain can be any area that can be described by right-angled polygons.
A typical solution on such a domain, with the grids used, looks like:
Local Uniform Grid Refinement:
Solution of PDE-system on one grid is done with the Method of Lines
- Start with a uniform base grid
- Compute solution on that grid
- Compute space monitor (based on the curvature)
- Where needed refine by bisection in every coordinate direction
- This gives a second grid (enclosed by the first one):
- also uniform
- cell-width halved
- Apply the same algorithm on the second grid
- This results in a series of nested grids where the PDE-system is solved
- Solution at the finest-mesh points is used
- Space discretization on a 9-point stencil (because of cross-derivatives).
Second-order finite differences.
- Resulting system of DAEs is solved with an implicit time-integrator (BDF2)
with variable stepsizes.
Algorithm 758: VLUGR2: A Vectorizable Adaptive Grid Solver for PDEs in 2D,
J.G. Blom, R.A. Trompert and J.G. Verwer
ACM Trans. Math. Softw., Vol. 22, No. 3, pp. 302-328 (1996).
Download software from ACM TOMS mirrorsites in:
VLUGR3: A Vectorizable Adaptive Grid Solver for PDEs in 3D.
I. Algorithmic Aspects and Applications,
J.G. Blom and J.G. Verwer
Appl. Numer. Math., Vol. 16, pp. 129-156 (1994).
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