Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications
Song JiangInstitute of Applied Physics and Computational Mathematics, Beijing, China
Jiequan LiInstitute of Applied Physics and Computational Mathematics, Beijing, China
Mária Lukáčová-Medvid’ováJohannes-Gutenberg-Universität Mainz, Germany
Gerald WarneckeOtto-von-Guericke University Magdeburg, Germany
This small collaborative workshop brought together experts from the Sino-German project working in the field of advanced numerical methods for hyperbolic balance laws. These are particularly important for compressible fluid flows and related systems of equations. The investigated numerical methods were finite volume/finite difference, discontinuous Galerkin methods, and kinetic-type schemes. We have discussed challenging open mathematical research problems in this field, such as multidimensional shock waves, interfaces with different phases or efficient and problem suited adaptive algorithms. Consequently, our main objective was to discuss novel high-order accurate schemes that reliably approximate underlying physical models and preserve important physically relevant properties. Theoretical questions concerning the convergence of numerical methods and proper solution concepts were addressed as well.
Cite this article
Song Jiang, Jiequan Li, Mária Lukáčová-Medvid’ová, Gerald Warnecke, Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications. Oberwolfach Rep. 18 (2021), no. 3, pp. 2269–2325DOI 10.4171/OWR/2021/41