论文标题
针对浅水方程的二维高阶良好平衡方案，具有地形和摩擦摩擦
A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction
论文作者
论文摘要
我们开发了一个二维高阶数值方案，该方案可以通过地形或摩擦摩擦准确保留并捕获浅水方程的移动稳态。高阶精度依赖于合适的多项式重建，而均衡性属性则基于Michel-Dansac等的一阶方案。 Al。，2016年和Michel-Dansac等。 Al。，2017年，扩展到两个空间维度。为了获得这两个属性，我们使用高阶方案和一阶均衡方案之间的凸组合。通过在非常简单的稳态检测器之后，充分选择凸组合参数，我们确保所得的方案既具有高级准确且平衡良好。然后，补充了一种情绪程序，以消除来自高阶多项式重建的虚假振荡，并保证溶液的物理可接受性。数值实验表明该方案确实具有声称的特性。关于实际数据的2011年日本海啸的模拟进一步证实了这一技术的相关性。
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable polynomial reconstruction, while the well-balancedness property is based on the first-order scheme from Michel-Dansac et. al., 2016 and Michel-Dansac et. al., 2017, extended to two space dimensions. To get both properties, we use a convex combination between the high-order scheme and the first-order well-balanced scheme. By adequately choosing the convex combination parameter following a very simple steady state detector, we ensure that the resulting scheme is both high-order accurate and well-balanced. The method is then supplemented with a MOOD procedure to eliminate the spurious oscillations coming from the high-order polynomial reconstruction and to guarantee the physical admissibility of the solution. Numerical experiments show that the scheme indeed possesses the claimed properties. The simulation of the 2011 Japan tsunami, on real data, further confirms the relevance of this technique.
