The Numerical Simulation of Radiative Shocks. I. The Elimination of Numerical Shock Instabilities Using a Local Oscillation Filter

We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density, and temperature are produced that are exacerbated by thermal instability when cooling is present, forming postshock "stripes." The resulting postshock striping substantially modifies the flow. We briefly review methods, based upon additional transverse dissipation, that have been introduced to counteract this instability. We then introduce a different method (a "local oscillation filter") based upon additional fluxes at the remapping stage of the PPM algorithm and compare this method to other approaches involving either grid-jittering or artificial diffusion. The test problem is a radiative wall shock with an embedded shear layer. Grid-jittering effectively counteracts striping. However, elsewhere on the grid, the shear layer is unphysically diffused and this is highlighted in an extreme case. The artificial diffusion method removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. The local oscillation filter performs slightly better in this regard but also does not broaden the shock, preserving the excellent shock capturing features of PPM. It also has the advantage of only acting on a smaller fraction of the cells in a two- or three-dimensional simulation.