The ADER approach in 2D for a system of linear hyperbolic PDEs. (English) Zbl 1028.76030

Sonar, Thomas (ed.) et al., Discrete modelling and discrete algorithms in continuum mechanics. Proceedings of the GAMM workshop, TU Braunschweig, Germany, November 24-25, 2000. Berlin: Logos Verlag. 207-216 (2001).
The paper presents an extension of ADER scheme to multi-dimensional cases. The method, which can be of arbitrary order in space and time, is outlined rather briefly for a hyperbolic linear system of PDEs. The functionality of the scheme is illustrated by two simple test cases involving linear advection equation in a square domain. The results indicate the great potential of the scheme. Possible extensions to more general geometrical situations involving non-Cartesian grids and/or more complex PDEs are not discussed.
For the entire collection see [Zbl 0971.00053].


76M12 Finite volume methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids