A Conservative Front Tracking Algorithm
Author(s)Nguyen, Vinh Tan; Khoo, Boo Cheong; Peraire, Jaime
The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.
High Performance Computation for Engineered Systems (HPCES);
conservative front tracking, conservative tracking in 2D, partial differential equations, numerical methods, laws of conservation