An explicit Mapped Tent Pitching scheme for hyperbolic systems

Abstract

272MinisymposiaAn explicit Mapped Tent Pitching scheme for hyperbolic systemsJay Gopalakrishnan1, Joachim Schöberl2, Christoph Wintersteiger2,∗1F. Maseeh Department of Mathematics and Statistics, Portland State University, Portland, USA2Institute for Analysis and Scientific Computing, TU Wien, Wien, Austria∗Email: christoph.wintersteiger@tuwien.ac.atAbstractThe presented Mapped Tent Pitching (MTP)method is based on a tent pitching algorithm,which partitions the spacetime domain into tent-shaped regions that respect causality. Instead ofdiscretizing these tents in spacetime, we intro-duce a transformation, which maps each tentto a domain with tensor product structure ofthe spatial domain with a time interval. Usinga discontinuous Galerkin method space, we ob-served a convergence order reduction when usingstandard explicit Runge-Kutta methods in time.Therefore we present a Runge-Kutta type time-stepping which overcomes this issue and can beapplied to non-linear hyperbolic systems.