An adaptive wavelet viscosity method for systems of hyperbolic conservation laws

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:240

Article

Heindl, Michael¹  Kunoth, Angela¹ 

[1] Univ Gesamthsch Paderborn, Inst Math, D-33098 Paderborn, Germany

关键词: Systems of conservation laws;    Viscosity method;    Adaptive wavelets;    Post-processing;   

DOI  :  10.1016/j.cam.2012.07.030

来源: Elsevier

【 摘 要 】

For the Burgers equation as an example of a hyperbolic conservation law, we have considered in our previous paper Castano Diez et al. (2008) [8] a weak formulation with a stabilization for handling discontinuities, commonly called a viscosity approach. Numerically, this was realized by locally introducing degrees of freedom around the discontinuities by means of an adaptive wavelet method in an a posteriori fashion. In the present paper, we apply this method to systems of conservation laws, specifically, Euler's equations for gas dynamics. Moreover, as the viscosity stabilization produces some Gibbs phenomena, we discuss different post-processing techniques known from data and image processing together with a number of numerical comparisons. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free