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On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems

机译:关于不可压缩对流-扩散输运和流体流动问题的稳定有限元公式

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A new approach is presented to obtain stabilized finite element formulations such as streamline-upwind/Petrov-Galerkin (SUPG) and Galerkin-least-squares (GLS). The procedure consists in modifying the equations to be solved and then obtaining the variational equations by the standard Galerkin method. The new formulation generates additional terms involving boundary integrals to standard stabilization techniques. These terms compensate for the lack of consistency of the traditional SUPG and GLS methods for which stabilization terms are added only on the element interiors, while jumps of the residual across element faces are neglected. A physical interpretation is provided of how the modified equations are obtained. It is shown how stabilized formulations Such as streamline- upwind (SU) and SUPG are recovered as special cases. Stabilization terms defined on the element interiors are always accompanied by additional boundary integrals. The presence of the boundary integrals is shown to improve the numerical prediction for various viscous and nearly inviscid flows.
机译:提出了一种获得稳定有限元公式的新方法,例如流线上风/ Petrov-Galerkin(SUPG)和Galerkin-最小二乘(GLS)。该过程包括修改要求解的方程,然后通过标准Galerkin方法获得变分方程。新公式生成了涉及标准稳定技术的边界积分的附加项。这些术语弥补了传统的SUPG和GLS方法缺乏一致性的问题,传统的SUPG和GLS方法仅在元素内部添加了稳定化术语,而忽略了跨元素面的残差跳跃。对如何获得修改后的方程式进行了物理解释。这表明在特殊情况下如何回收稳定的配方,例如流线逆风(SU)和SUPG。在单元内部定义的稳定项始终带有附加的边界积分。边界积分的存在可以改善各种粘性和几乎不粘流的数值预测。

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