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Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations. (English) Zbl 1370.76116
Summary: The numerical simulation of physical phenomena represented by non-linear hyperbolic systems of conservation laws presents specific difficulties mainly due to the presence of discontinuities in the solution. State of the art methods for the solution of such equations involve high resolution shock capturing schemes, which are able to produce sharp profiles at the discontinuities and high accuracy in smooth regions, together with some kind of grid adaption, which reduces the computational cost by using finer grids near the discontinuities and coarser grids in smooth regions. The combination of both techniques presents intrinsic numerical and programming difficulties. In this work we present a method obtained by the combination of a high-order shock capturing scheme, built from C.-W. Shu and S. Osher’s conservative formulation [J. Comput. Phys. 77, No. 2, 439–471 (1988; Zbl 0653.65072); ibid. 83, No. 1, 32–78 (1989; Zbl 0674.65061)], a fifth-order weighted essentially non-oscillatory (WENO) interpolatory technique [G.-S. Jiang and C.-W. Shu, ibid. 126, No. 1, 202–228 (1996; Zbl 0877.65065)] and R. Donat and A. Marquina’s flux-splitting method [ibid. 125, No. 1, 42–58 (1996; Zbl 0847.76049)], with the adaptive mesh refinement (AMR) technique of M. J. Berger and collaborators [with P. Colella, ibid. 82, No. 1, 64–84 (1989; Zbl 0665.76070); with J. Oliger, ibid. 53, 484–512 (1984; Zbl 0536.65071); M. J. Berger, Adaptive mesh refinement for hyperbolic partial differential equations. Stanford, CA: Stanford University. (PhD Thesis) (1982)].

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76L05 Shock waves and blast waves in fluid mechanics
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References:
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