...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Computational Physics >An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations withcomplete Coriolis force
【24h】

An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations withcomplete Coriolis force

机译：具有完全科里奥利力的多层浅水方程组的能量和势能熵守恒数值格式

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We present an energy- and potential enstrophy-conserving scheme for the non-traditional shallow water equations that include the complete Coriolis force and topography. These integral conservation properties follow from material conservation of potential vorticity in the continuous shallow water equations. The latter property cannot be preserved by a discretisation on a fixed Eulerian grid, but exact conservation of a discrete energy and a discrete potential enstrophy seems to be an effective substitute that prevents any distortion of the forward and inverse cascades in quasi-two dimensional turbulence through spurious sources and sinks of energy and potential enstrophy, and also increases the robustness of the scheme against nonlinear instabilities. We exploit the existing Arakawa-Lamb scheme for the traditional shallow water equations, reformulated by Salmon as a discretisation of the Hamiltonian and Poisson bracket for this system. The non-rotating, traditional, and our non-traditional shallow water equations all share the same continuous Hamiltonian structure and Poisson bracket, provided one distinguishes between the particle velocity and the canonical momentum per unit mass. We have determined a suitable discretisation of the non-traditional canonical momentum, which includes additional coupling between the layer thickness and velocity fields, and modified the discrete kinetic energy to suppress an internal symmetric computational instability that otherwise arises for multiple layers. The resulting scheme exhibits the expected second-order convergence under spatial grid refinement. We also show that the drifts in the discrete total energy and potential enstrophy due to temporal truncation error may be reduced to machine precision under suitable refinement of the timestep using the third-order Adams-Bashforth or fourth-order Runge-Kutta integration schemes. (C) 2016 Elsevier Inc. All rights reserved.
机译：对于非传统的浅水方程，我们提出了一种能量和潜在的熵守恒方案，其中包括完整的科里奥利力和地形。这些积分守恒性质来自连续浅水方程中潜在涡度的物质守恒。后者的特性不能通过在固定的欧拉网格上离散化来保留，但是离散能量的精确守恒和离散潜在的涡旋似乎是防止准二维湍流中正向和反向级联发生任何扭曲的有效替代方法。虚假的能量源和能量汇和潜在的回旋，还提高了该方案针对非线性不稳定性的鲁棒性。我们将现有的Arakawa-Lamb方案用于传统的浅水方程，由Salmon重新公式化为该系统的Hamiltonian和Poisson括号的离散化。非旋转的，传统的和我们的非传统浅水方程组都具有相同的连续哈密顿结构和泊松括号，条件是要区分粒子速度和单位质量的规范动量。我们已经确定了非传统规范动量的适当离散化，其中包括层厚度和速度场之间的附加耦合，并修改了离散动能以抑制内部对称的计算不稳定性，否则这种不稳定性会出现在多层中。所得方案在空间网格细化下表现出预期的二阶收敛性。我们还表明，在使用三阶Adams-Bashforth或四阶Runge-Kutta积分方案对时间步长进行适当调整的情况下，由于时间截断误差而导致的离散总能量和潜在的熵的漂移可能会降低到机器精度。 （C）2016 Elsevier Inc.保留所有权利。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号