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hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow

机译：hp间断Galerkin方法求解浅水流动中对流占优的问题

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摘要

In this paper, we discuss the development, verification, and application of an hp discontinuous Galerkin (DG) finite element model for solving the shallow water equations (SWE) on unstructured triangular grids. The h and p convergence properties of the method are demonstrated for both linear and highly nonlinear problems with advection dominance. Standard h-refinement for a fixed p leads to p + 1 convergence rates, while exponential convergence is observed for p-refinement for a fixed h. It is also demonstrated that the use of p-refinement is more efficient for problems exhibiting smooth solutions. Additionally, the ability of p-refinement to adequately resolve complex, two-dimensional flow structures is demonstrated in the context of a coastal inlet problem.
机译：在本文中，我们讨论了用于解决非结构化三角网格上的浅水方程（SWE）的hp不连续Galerkin（DG）有限元模型的开发，验证和应用。对于具有对流优势的线性和高度非线性问题，都证明了该方法的h和p收敛性质。固定p的标准h细化导致p +1收敛速度，而固定h的p细化观察到指数收敛。还表明，对于显示平滑解的问题，使用p精炼更为有效。此外，在沿海进口问题的背景下，证明了p精制能够充分解决复杂的二维流动结构的能力。

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