Donna Calhoun,
Randall J. LeVeque
Solving Hyperbolic Problems on Adaptive Mapped Grids in Two and Three Dimensions
We are currently studying some of the issues related to solving
hyperbolic problems on mapped two and three dimensional
logically-rectangular grids, using the wave-propagation algorithm
implemented in CLAWPACK and various adaptive versions of this code
(AMRCLAW, BEARCLAW and CHOMBO-CLAW). We solve the original PDE in
physical coordinates, but solve Riemann problems in directions aligned
with the underlying mapped grid. Our current goal is to gain more
understanding of the accuracy and conservation properties of this approach
and to test it carefully on a variety of hyperbolic problems arising in
applications. In particular, we are investigating the accuracy
of our conservative fix-up at coarse/fine grid interfaces.