Stabilized residual distribution for shallow water simulations
Stabilized residual distribution for shallow water simulations
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DOI：
10.1016/j.jcp.2008.10.020
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
M. Ricchiuto;A. Bollermann
中科院分区：
文献类型：
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作者：
M. Ricchiuto;A. Bollermann
我们提出了一种稳定残差分布（RD）方案来模拟浅水流动。最后的离散化是结合（Abgrall， J. Comp. Phys. 214, 2006）和（Ricchiuto and Abgrall, ICCFD4, Springer-Verlag 2006）中提出的稳定RD方法，以及（Ricchiuto et al.， J. Comp. Phys. 222, 2007）中已经使用的保守公式来模拟浅水流动。该方法是一种非线性的拉克斯-弗里德里希离散化方法。它很好地平衡，它实际上在光滑区域产生二阶精度，并且在干燥区域存在时它保留了水的高度的正性。这可以通过离散化的残差特性，通过适当地适应（Abgrall， J. Comp. Phys. 214, 2006）和（Ricchiuto和Abgrall， ICCFD4, Springer-Verlag, 2006）中提出的稳定算子，以及底层Lax-Friedrichs方案的正保持特性来实现。我们在各种各样的测试中证明了离散化的性质。
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 (Ricchiuto 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 on a wide variety of tests.