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Stabilized residual distribution for shallow water simulations

机译:浅水模拟的稳定残留分布

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摘要

We propose a stabilized Residual Distribution (RD) scheme for the simulation of shallow water flows. The final discretization is obtained combining the stabilized RD approach proposed in (Abgrall, J. Comp. Phys. 214, 2006) and (Ricclliuto and Abgrall, ICCFD4, Springer-Verlag 2006), with the conservative formulation already used in (Ricchiuto et al., J. Comp. Phys. 222, 2007) to simulate shallow water flows. The scheme proposed is a nonlinear variant of a Lax-Friedrichs type discretization. It is well balanced, it actually yields second-order of accuracy in smooth areas, and it preserves the positivity of the height of the water in presence of dry areas. This is made possible by the residual character of the discretization, by properly adapting the stabilization operators proposed in (Abgrall, J. Comp. Phys. 214, 2006) and (Ricchiuto and Abgrall, ICCFD4, Springer-Verlag, 2006), and thanks to the positivity preserving character of the underlying Lax-Friedrichs scheme. We demonstrate the properties of the discretization proposed oil a wide variety of tests. (C) 2008 Elsevier Inc. All rights reserved.
机译:我们提出了一种稳定的剩余分布(RD)方案来模拟浅水流动。将(Abgrall,J.Comp.Phys.214,2006)和(Ricclliuto and Abgrall,ICCFD4,Springer-Verlag 2006)中提出的稳定RD方法与(Ricchiuto等(J. Comp。Phys。222,2007)来模拟浅水流。提出的方案是Lax-Friedrichs类型离散化的非线性变体。它具有很好的平衡性,在光滑区域中实际上可以产生二阶精度,并且在干燥区域中可以保持水高的正值。通过离散化的剩余特征,通过适当地修改(Abgrall,J. Comp。Phys。214,2006)和(Ricchiuto and Abgrall,ICCFD4,Springer-Verlag,2006)中提出的稳定化算子,可以实现这一点。底层Lax-Friedrichs方案的正性保留特性。我们通过各种测试证明了离散化建议油的特性。 (C)2008 Elsevier Inc.保留所有权利。

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