论文标题
提高矢量传输方程在最低阶的四边形 - thomas thomas有限元的准确性
Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements
论文作者
论文摘要
在流体的有限元模型中，使用raviart-thomas元素通常会离散速度或动量变量等矢量估算场。但是，当使用最低的四边形raviart-thomas元素时，矢量传输方程的标准有限元离散通常具有低空间精度。本文介绍了两种方案，这些方案提高了在二维弯曲歧管上运输此矢量值磁场的准确性。 提出的第一个方案在高阶函数空间中重建了传输场，然后在该空间中求解了传输方程。第二个方案将混合有限元公式应用于矢量传输方程，同时求解了运输场及其涡度。提出了一种稳定这种混合矢量涡流配方的方法，该方法使用了流线上的petrov-galerkin（SUPG）方法。然后，通过一些数值测试来证明这些方案以及它们的准确性。两个新的测试用例用于评估弯曲流形上矢量值磁场的运输，从而孤立地求解了矢量传输方程。还通过两个用于旋转浅水模型的标准测试用例显示了方案的改进。
Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. An approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.
