Level Set Algorithm for Tracking Shock in Hyperbolic Conservation Laws for Multi dimensional Scalar Equations
Feng Jianhu(1,2),Cai Li(2),Wang Zhenhai(2),She Hongwei(2)
(1 Chang An University, Xi'an, 710064) (2 Northwestern Polytechnical University, Xi'an, 710072)

Abstract: To track shock waves effectively in hyperbolic conservation laws in one-dimensional cases, fourth-order accurate CWENO (Central Weighted Essentially Non-Oscillatory) scheme is used together with the fourth-order accurate NCE (Natural Continuous Extensions) Runge-Kutta scheme and the Level Set algorithm. Combined the fifth-order WENO (Weighted Essentially Non-Oscillat ory) scheme with the non-TVD fourth-order Runge-Kutta scheme and the Level Set algorithm, two-dimensional cases are solved successfully. The solutions are compared with standard high order shock capturing schemes, it indicates that Level Set tracking schemes are effective ones with high order pointwise convergence quality.
Keywords: shock capturing, WENO, CWENO, level set.