These lectures will describe simple upwind difference schemes for scalar conservation laws where flux interfaces are present. The primary focus will be on interfaces caused by jumps in spatially varying flux parameters, but network junctions will also be addressed. The unifying design principles of these algorithms are that they are upwind, and that the flux interfaces are "hidden" within the interiors of the computational cells. This treatment of flux interfaces results in schemes requiring only familiar 1D upwind fluxes such as Godunov or Engquist-Osher. The algorithms have interesting analytical properties including conservation-form, monotonicity, and maximum principles. Convergence results will be presented, including a discussion of the "singular mapping", along with its connection to the Kruzkov entropy flux, and the Engquist-Osher numerical flux.

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Helge Holden <holden@math.ntnu.no>

2000-09-22 08:32