Mesh‐free properties are part of the superiority of cell‐based smoothed finite element method (CS‐FEM), but have yet to be fully exploited for computational fluid dynamics. A novel implementation of CS‐FEM for incompressible viscous fluid flows in stationary and deforming domains discretized by severely distorted bilinear four‐node quadrilateral (Q4) elements is presented in this article. The negative determinant of the Jacobian transformation from the Cartesian coordinates to the natural coordinates is intentionally stipulated for the corresponding mesh over which FEM inevitably fails in practice. It is found that, without ad hoc modifications, CS‐FEM incurs unsatisfactory results and even a failure on fixed meshes. To cater for general computations on either a uniform or nonuniform mesh represented by these badly degenerated elements, four smoothing cells (SCs) are deployed in convex Q4 element whereas one SC in concave Q4 element. A simple hourglass control is introduced into those under‐integrated quadrilaterals for stabilizing the one‐SC quadrature in smoothed Galerkin weak form. Thanks to the adoption of characteristic‐based split (CBS) scheme for the fluid solution, a byproduct is the unfolded equivalence of the CBS stabilization and balancing tensor diffusivity under the incompressibility constraint. Several benchmark problems involving incompressible fluid flow and fluid‐structure interaction are solved. Numerical results show the good accuracy and robustness of the proposed approach that raises a seductive idea for resolving moving‐mesh problems.

中文翻译：

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基于单元的平滑有限元方法的网格变形的真正实现，适用于具有固定边界和移动边界的不可压缩流体

无网格特性是基于单元的平滑有限元方法（CS-FEM）优势的一部分，但尚未完全用于计算流体动力学。本文介绍了一种CS-FEM的新颖实现方式，该解决方案用于在严重变形的双线性四节点四边形（Q4）元素离散的固定和变形域中的不可压缩粘性流体流动。该负对于相应的网格，特意规定了从笛卡尔坐标到自然坐标的雅可比变换的决定因素，而有限元在实践中不可避免地会失败。结果发现，如果不进行临时修改，CS-FEM的结果将不能令人满意，甚至在固定网格上也会失败。为了满足由这些严重退化的元素表示的均匀或不均匀网格上的常规计算，在凸Q4元素中部署了四个平滑单元（SC），而在凹Q4元素中部署了一个SC。在那些积分不足的四边形中引入了一个简单的沙漏控制，以稳定化的Galerkin弱形式稳定one-SC正交。由于流体解决方案采用了基于特征的拆分（CBS）方案，副产品是在不可压缩性约束下CBS稳定和平衡张量扩散率的展开等价性。解决了涉及不可压缩流体流动和流体-结构相互作用的几个基准问题。数值结果表明，该方法具有良好的准确性和鲁棒性，提出了解决运动网格问题的诱人方法。