论文标题
用于椭圆形问题和应用垂直海洋式建模的混合不连续的盖金方法
The Hybrid Discontinuous Galerkin method for elliptic problems and applications in vertical ocean-slice modeling
论文作者
论文摘要
元素方法。有限体积方法保证了本地和全球群众保护。有限体积方法不满足的属性。在下侧，有限体积方法需要非微不足道的修改才能获得高阶近似值，这与有限体积方法不同。有人认为，不连续的盖尔金方法，局部保守和高级，是沿海海洋建模的自然发展。因此，作为底漆，我们考虑具有密度效应的垂直海洋式式模型。为了解决这些非稳定的偏微分方程，我们开发了一种解决方案的压力投影方法。我们在每个时间步骤中提出了一个杂交的不连续的盖尔金解决方案，以解决所需的泊松问题。目的是降低不连续盖尔金方法的经典应用的计算成本。杂交不连续的盖金方法首先作为一般的椭圆问题解决者提出。结果表明，高阶实现在粗网格上可以快速准确地近似。
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.
