## Local Uniform Grid Refinement:

- 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
in succession
- Solution at the finest-mesh points is used

Solution of PDE-system on one grid is done with the Method of Lines
principle
- Space discretization on a 9-point stencil in 2D or a 19-point stencil in 3D
(because of cross-derivatives).
Second-order finite differences.
- Resulting system of DAEs is solved with an implicit time-integrator (BDF2)
with variable stepsizes.

Go to the
LUGR page,
or to the
CWI Mathematics & the Environment program overview,
or to the
CWI home page.

Joke Blom
(gollum@cwi.nl)
Last update 95/02/17.