Metric-discontinuous zonal grid calculations using the Osher scheme

Computations on zonal grids—in particular, grids with metric discontinuities resulting from the interspersion of highly clustered regions with coarse regions—are possible using a fully conservative form of the Osher upwind scheme. These zonal grids can result from an abrupt clustering of points near solution discontinuities or near other flow features that require improved resolution. The zonal approach is shown to capture shocks with almost “shock-fitting” quality but with minimal effort. Results for inviscid flow, including quasi-one-dimensional nozzle flow, supersonic flow over a cylinder, and blast-wave diffraction by a ramp, are presented. These calculations demonstrate the powerful capabilities of the Osher scheme used in conjunction with zonal grids in simulating flow fields with complex shock patterns.