ABSTRACT
Gravity waves arise in gravitationally stratified compressible flows at low Mach and Froude numbers, and these waves impose a sharp restriction on the time step. This paper presents a filtering strategy for the fully compressible equations based on normal-mode analysis that is used throughout the simulation to compute the fast dynamics and is able to damp only chosen modes. This method is based on an asymptotic analysis and respects the dynamics of gravity waves for thin layers. Finally, the filtering method is tested on a series of examples.
ABSTRACT
We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based on level set methods for solving the Hamilton-Jacobi and eikonal equations. We demonstrate that the method is second-order accurate in space and time and is capable of computing solutions on complex surface geometries obtained from image data of cells.
