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首页> 外文期刊>Journal of Computational Physics >A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations
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A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations

机译：浅水方程组的半隐式，半拉格朗日，p自适应不连续Galerkin方法

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摘要

A semi-implicit and semi-Lagrangian discontinuous Galerkin method for the shallow water equations is proposed, for applications to geophysical scale flows. A non conservative formulation of the advection equation is employed, in order to achieve a more treatable form of the linear system to be solved at each time step. The method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution. Numerical results show that the method captures well the main features of gravity and inertial gravity waves, as well as reproducing correct solutions in nonlinear test cases with analytic solutions. The accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree.
机译：提出了一种浅水方程的半隐式和半拉格朗日间断Galerkin方法，用于地球物理尺度流。为了获得在每个时间步求解的线性系统的更易于处理的形式，采用对流方程的非保守公式。该方法配备有简单的p适应性准则，该准则允许动态地调整对解决方案的局部结构采用的局部自由度的数量。数值结果表明，该方法很好地捕捉了重力波和惯性重力波的主要特征，并利用解析解再现了非线性测试案例中的正确解。该方法的准确性和有效性还通过在高库兰特数下获得的数值结果以及自动选择局部逼近度来证明。

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