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首页> 外文期刊>International Journal for Numerical Methods in Fluids >The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier-Stokes equations
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The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier-Stokes equations

机译：Navier-Stokes方程的三维长时间自适应非结构​​化有限元多重网格方法

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This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier-Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow.
机译：本文介绍了用于Navier-Stokes方程的三维加长型自适应有限元方程求解器的开发。所使用的有限元是四面体，其速度近似为平方，压力近似为线性。方程组由基本变量组成。通过元素雷诺数使网格适合解决方案。当元素的雷诺数超过预设限制时，将优化网格中的元素。通过将解决方案缩放为较低的雷诺数，可以增加调查中的全局雷诺数。根据缩放后的解精炼网格，较低的雷诺数的延长解构成较高雷诺数的起始向量。由于雷诺数是对流与扩散的比率，因此网格细化充当了方程组的线性化和对称化。牛顿公式的线性方程组由CGSTAB和耦合节点填充前置条件求解。考虑的测试问题是三维驱动腔流动。

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