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Mass Conservation of the Unified Continuous and Discontinuous Element-Based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations.

机译：基于统一连续和不连续单元的动态自适应网格Galerkin方法的质量守恒应用于大气模拟。

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We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG) Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The two methods are implemented in a unified way which allows for a direct comparison of the non-conforming edge treatment. We outline the implementation details of the non-conforming direct stiffness summation algorithm for the CG method and show that the mass conservation error is similar to the DG method. Both methods conserve to machine precision, regardless of the presence of the non-conforming edges. For lower order polynomials the CG method requires additional stabilization to run for very long simulation times. We addressed this issue by using filters and/or additional artificial viscosity. The mathematical proof of mass conservation for CG with non-conforming meshes is presented in Appendix B.

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Kopera, M. A.; Giraldo, F. X.;
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年度 2015
页码 1-18
总页数 18
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Atmospherics; Galerkin method; Grids; Algorithms; Boundary layer; Differential geometry; Euler equations; Geophysics; Mathematical models; Matrices(mathematics); Mesh; Polynomials; Simulation; Stabilization; Temperature; Test and evaluation; Vector analysis; Velocity; Viscosity; Adaptive mesh refinement; Cg(continuous galerkin); Dg(discontinuous galerkin); Non-conforming mesh; Compressible euler equations; Atmospheric simulations; Pe0602435n;

机译：大气; Galerkin方法;网格;算法;边界层;微分几何;欧拉方程;地球物理学;数学模型;矩阵（数学）;网格;多项式;模拟;稳定;温度;测试和评估;矢量分析;速度;粘度;自适应网格细化; Cg（连续galerkin）; Dg（不连续galerkin）;不符合网格;可压缩欧拉方程;大气模拟; pe0602435n;

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专利

1. Mass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations [J] . Kopera Michal A., Giraldo Francis X. Journal of Computational Physics . 2015,第Null期

机译：动态自适应网格上基于连续和不连续元素的统一Galerkin方法的质量守恒及其在大气模拟中的应用
2. Simulation of shallow-water jets with a unified element-based continuous/discontinuous Galerkin model with grid flexibility on the sphere [J] . Marras S., Kopera M. A., Giraldo F. X. Quarterly Journal of the Royal Meteorological Society . 2015,第690aPta1期

机译：使用基于单元的统一连续/不连续Galerkin模型模拟球面网格的浅水射流
3. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids [J] . Wang Z.J., Gao H. Journal of Computational Physics . 2009,第21期

机译：统一的提升搭配罚分公式，包括不连续Galerkin，混合网格守恒律的频谱体积/差异方法
4. Discontinuous Galerkin methods for mass conservation equations for environmental modeling [C] . M.J. Guillot, B. Riviere, M.F. Wheeler XIVth International Conference on Computational Methods in Water Resources (CMWR XIV), Jun 23-28, 2002, Delft, The Netherlands . 2002

机译：用于环境建模的质量守恒方程的不连续Galerkin方法
5. A unified mathematical framework of continuous and discontinuous time integrators and domain decomposition techniques for scalable high performance structural dynamics simulations. [D] . Kanapady, Ramdev. 2001

机译：连续和不连续时间积分器和域分解技术的统一数学框架，用于可扩展的高性能结构动力学仿真。
6. A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws [O] . Zhiliang Xu, Xu-Yan Chen, Yingjie Liu -1

机译：具有守恒约束的Runge-Kutta间断Galerkin新方法可改善CFL条件以求解守恒律
7. Mass Conservation of the Unified Continuous and Discontinuous Element-Based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations [O] . Kopera Michal A., Giraldo Francis X. 2015

机译：动态连续网格上基于连续和不连续元素的统一Galerkin方法的质量守恒及其在大气模拟中的应用

Mass Conservation of the Unified Continuous and Discontinuous Element-Based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations.

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