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

Pep Mulet () and Antonio Baeza ()
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Pep Mulet: Universitat de València, Departament de Matemàtica Aplicada
Antonio Baeza: Universitat de València, Departament de Matemàtica Aplicada

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 198-206 from Springer

Abstract: Abstract 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.

Keywords: Coarse Grid; Riemann Problem; Adaptive Mesh; Grid Algorithm; Flux Reconstruction (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/978-3-540-34288-5_12

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