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Two-dimensional compact third-order polynomial reconstructions. Solving nonconservative hyperbolic systems using GPUs. (English) Zbl 1426.76366
Summary: We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in [M. J. Castro et al., ibid. 39, No. 1, 67–114 (2009; Zbl 1203.65131)] for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.

76M12 Finite volume methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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