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.
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References
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Mulet, P., Baeza, A. (2006). Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_12
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DOI: https://doi.org/10.1007/978-3-540-34288-5_12
Publisher Name: Springer, Berlin, Heidelberg
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