We present a fully conservative, high resolution approach to front tracking for nonlinear systems of conservation laws in two space dimensions. An underlying uniform Cartesian grid is used, with some cells cut by the front into two subcells. The front is moved by solving a Riemann problem normal to each segment of the front and using the motion of the strongest wave to give an approximate locat...

Numerical simulations of a spherical shock refraction have been successfully conducted by a front tracking method We demonstrate the e ciency of the front tracking algorithm by comparing the L error of spherical simulations by tracked and untracked methods We nd that the tracked algorithm is about times faster than the correspond ing method without tracking the interface for a d d simulation

Abstract. Accurate modeling of flooding and drying is important in forecasting river floods and near-shore hydrodynamics. We consider the space-time discontinuous Galerkin finite element discretization for shallow water equations with linear approximations of flow field. In which, the means (zeroth order approximation) is used to conserve the mass and momentum, and the slopes (first order appro...

We describe a three dimensional front tracking algorithm, discuss its numerical implementation, and present studies to validate the correctness of this approach. Based on the results of the two dimensional computations, we expect three dimensional front tracking to improve signiicantly computational eeciencies for problems dominated by discontinu-ities. In some cases, for which the interface co...

We propose and study parallel numerical algorithms for simulation of flows with elastic membranes, such as red blood cells. The challenges of modeling such flows include accurately resolving the interface motion and enforcing the appropriate interface mechanics. We propose a phase field Eulerian method for implicitly capturing the location of the dynamic interface between two fluids. In additio...