论文标题
几何参数化的Stokes流动的杂交不连续的galerkin解决方案
Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows
论文作者
论文摘要
本文提出了一个新的计算框架，用于解决由Stokes方程控制的几何参数化流问题。所提出的方法使用高阶杂交不连续的Galerkin公式和适当的广义分解理由来为给定的一组几何参数构建离线解决方案。广义解决方案包含用户定义范围内所有几何参数的信息，并且可以用于计算灵敏度。所提出的方法基于适当的一般性分解来规避其他方法的许多弱点，用于计算几何参数性问题的通用解。四个数值示例显示了所提出的方法的最佳近似属性，并在两个和三个维度中证明了其适用性。
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an off-line solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a user-defined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal approximation properties of the proposed method and demonstrate its applicability in two and three dimensions.
