Element Method. The Finite Volume Method guarantees local and global mass conservation. A property not satisfied by the Finite Volume Method. On the down side, the Finite Volume Method requires non trivial modifications to attain high order approximations unlike the Finite Volume Method. It has been contended that the Discontinuous Galerkin Method, locally conservative and high order, is a natural progression for Coastal Ocean Modeling. Consequently, as a primer we consider the vertical ocean-slice model with the inclusion of density effects. To solve these non steady Partial Differential Equations, we develop a pressure projection method for solution. We propose a Hybridized Discontinuous Galerkin solution for the required Poisson Problem in each time step. The purpose, is to reduce the computational cost of classical applications of the Discontinuous Galerkin method. The Hybridized Discontinuous Galerkin method is first presented as a general elliptic problem solver. It is shown that a high order implementation yields fast and accurate approximations on coarse meshes.
翻译:元素量方法。 精度量方法保证了本地和全球的大规模保护。 一种财产不为精度量方法所满足。 在下方, 精度量方法要求非微小的修改, 以达到与精度量方法不同的高排序近似值。 有人争辩说, 本地保守和高排序的不连续的加勒金方法是沿海海洋建模的自然进步。 因此, 作为入门器, 我们考虑垂直的海洋切除模型, 并纳入密度效应。 为了解决这些不稳定的局部差异, 我们开发了一种压力预测方法。 我们为所要求的 Poisson 问题建议了一种混合不连续的加勒金解决方案, 目的是降低不连续加勒金方法的典型应用的计算成本。 混合不连续加勒金方法首先作为一般的椭圆问题解算器提出。 显示, 高顺序执行率能快速准确地接近粗度的 meshes。