Finite-volume solutions

to hyperbolic PDEs

by Dr Donna Calhoun and Dr David George

Department of Mathematics, Boise State University (Calhoun) & U.S. Geological Survey (George)


(1) General principles of solving one-dimensional linear and quasi-linear hyperbolic systems using finite volume methods

  • Particular focus will be given to the wave propagation algorithms (R. J. LeVeque) and the discussion of second order corrections and limiters.

(2) Extensions of the wave propagation algorithm to shallow water equations using Roe-linearization

  • Extensions to two-dimensional problems.

(3) Principles of patch-based adaptive mesh refinement (AMR)

(4) Introduction to GeoClaw