6533b831fe1ef96bd129836b

RESEARCH PRODUCT

Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws

Pep MuletAntonio Baeza

subject

Scheme (programming language)Conservation lawMathematical optimizationAdaptive mesh refinementComputer scienceFinite differenceMathematics::Numerical Analysislaw.inventionShock (mechanics)symbols.namesakeRiemann problemlawsymbolsApplied mathematicsPolygon meshCartesian coordinate systemcomputercomputer.programming_language

description

We review a conservative finite difference shock capturing scheme that has been used by our research team over the last years for the numerical simulations of complex flows [3, 6]. This scheme is based on Shu and Osher’s technique [9] for the design of highly accurate finite difference schemes obtained by flux reconstruction procedures (ENO, WENO) on Cartesian meshes and Donat-Marquina’s flux splitting [4]. We then motivate the need for mesh adaptivity to tackle realistic hydrodynamic simulations on two and three dimensions and describe some details of our Adaptive Mesh Refinement (AMR) ([2, 7]) implementation of the former finite difference scheme [1]. We finish the work with some numerical experiments that show the benefits of our scheme.

yearjournalcountryeditionlanguage
2007-10-07
https://doi.org/10.1007/978-3-540-34288-5_12