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High-Resolution Multimesh hp-FEM for Simulation of Compressible Particle-Laden Gas Flows

用于模拟可压缩颗粒加载气流的高分辨率多网格 hp-FEM

基本信息

批准号：
195871519
负责人：
Professor Dr. Dmitri Kuzmin
金额：
--
依托单位：
Department of Mathematics and Statistics
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2011
资助国家：
德国
起止时间：
2010-12-31 至 2015-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/195871519?language=en
关键词：
Resolution Multimesh hp FEM Simulation

项目摘要

The objective of this project is the development of a new approach to hp-adaptivity for scalar transport equations and hyperbolic systems on the basis of methods implemented during the first funding period. The proposed variational multiscale framework will combine a continuous Galerkin approximation of coarse scales with a discontinuous approximation of fine scales. To this end, continuous (P1 or Q1) finite elements will be enriched by Taylor basis functions that have been employed to design hierarchichal slope limiting techniques for p-adaptive discontinuous Galerkin (DG) methods. At the coarse scale level, the discrete maximum principle will be enforced using an algebraic flux correction scheme of FCT type (Flux-Corrected Transport). The multimesh hp-FEM approach implemented in the software package HERMES makes it possible to use individually designed meshes for each variable and each level of the p-hierarchy. The type of adaptivity (h or p) is determined using maximum principles to estimate the local regularity. The process of smoothness and error estimation involves the use of reconstruction techniques for the highest-order derivatives. The decomposition of the nonlinear system into a global problem for the coarse scales and small local problems for the fine scales offers substantial efficiency gains. The extension of the new hp-FEM to the Euler equations and equations of the two-fluid modell will build on the previously developed numerical algorithms for coarse-scale simulations.

该项目的目标是在第一个资助期内实施的方法的基础上，为标量输运方程和双曲系统开发一种新的hp自适应方法。拟议的变分多尺度框架将结合联合收割机连续Galerkin近似的粗尺度与不连续近似的细尺度。为此，连续（P1或Q1）有限元将丰富的泰勒基函数，已被用来设计hierarchichal斜率限制技术的p-自适应间断伽辽金（DG）方法。在粗尺度水平上，将使用FCT类型的代数通量校正方案（通量校正传输）来执行离散最大值原理。在软件包爱马仕中实现的多网格hp-FEM方法使得有可能使用单独设计的网格为每个变量和每个层次的p-层次。使用最大值原理来估计局部正则性，从而确定自适应性的类型（h或p）。平滑和误差估计的过程涉及使用最高阶导数的重构技术。将非线性系统分解为粗尺度的全局问题和细尺度的小局部问题提供了大量的效率增益。新的hp-FEM扩展到欧拉方程和双流体模型方程将建立在先前开发的粗尺度模拟的数值算法上。