Seminar in Numerical Analysis: Armin Iske (Universität Hamburg)

Ten good reasons for using kernel reconstructions in adaptive finite volume particle methods

This talk discusses the utility of meshfree kernel techniques in adaptive finite volume particle methods (FVPM). To this end, we give ten good reasons in favour of using kernel-based reconstructions in the recovery step of FVPM, where our discussion addresses relevant computational aspects concerning numerical stability and accuracy, as well as more specific points concerning efficient implementation. Special emphasis is finally placed on morerecent advances in the construction of adaptive FVPM, where WENO reconstructions by polyharmonic spline kernelsare used in combination with ADER flux evaluations to obtain high order methods for hyperbolic problems.

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