An adaptive wavelet viscosity method for systems of hyperbolic conservation laws

• Autores: Michael Heindl, Angela Kunoth
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 240, Nº 1, 2013, págs. 215-224
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.07.030
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• Resumen

  • For the Burgers equation as an example of a hyperbolic conservation law, we have considered in our previous paper Castaño Díez 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.