A Quadtree Adaptive Level Set Method for Capturing Interfacial Instability On Cartesian Grid

Abstract

A high order finite volume difference scheme is combined with a quadtree level set adaptive mesh refinement to solve compressible multi-fluid interfacial instability problems that require high order accuracy interfaces in space. The solution scheme for the fluid dynamics equations and algorithm of the quadtree adaptive level set method for capturing interfaces are presented. To verify and validate this method, the numerical results of an experiment of a shock-accelerated heavy gas cylinder conducted by State University of New York at Stony Brook are given, and compared with simulations documented in this paper. Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz compressible multi-fluid interfacial instability examples are calculated too. The accurate positions of the interfaces are captured by level set method adaptively using the fixed Cartesian grids.