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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Collision in a cross-shaped domain - A steady 2d Navier-Stokes example demonstrating the importance of mass conservation in CFD
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Collision in a cross-shaped domain - A steady 2d Navier-Stokes example demonstrating the importance of mass conservation in CFD

机译：十字形区域中的碰撞-一个稳定的二维Navier-Stokes示例，展示了CFD中质量守恒的重要性

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摘要

In the numerical simulation of the incompressible Navier-Stokes equations different numerical instabilities can occur. While instability in the discrete velocity due to dominant convection and instability in the discrete pressure due to a vanishing discrete Ladyzhenskaya-Babuska-Brezzi (LBB) constant are well-known, instability in the discrete velocity due to a poor mass conservation at high Reynolds numbers sometimes seems to be underestimated. At least, when using conforming Galerkin mixed finite element methods like the Taylor-Hood element, the classical grad-div stabilization for enhancing discrete mass conservation is often neglected in practical computations. Though simple academic flow problems showing the importance of mass conservation are well-known, these examples differ from practically relevant ones, since specially designed force vectors are prescribed. Therefore, we present a simple steady Navier-Stokes problem in two space dimensions at Reynolds number 1024, a colliding flow in a cross-shaped domain, where the instability of poor mass conservation is studied in detail and where no force vector is prescribed.
机译：在不可压缩的Navier-Stokes方程的数值模拟中，可能会出现不同的数值不稳定性。众所周知，由于主导对流造成的离散速度不稳定和离散Ladyzhenskaya-Babuska-Brezzi（LBB）常数消失导致的离散压力不稳定，但由于在高雷诺数下质量守恒性较差，因此离散速度不稳定有时似乎被低估了。至少，当使用诸如泰勒-霍德（Taylor-Hood）元素之类的符合标准的Galerkin混合有限元方法时，用于提高离散质量守恒性的经典grad-div稳定在实际计算中常常被忽略。尽管显示质量守恒重要性的简单学术流程问题是众所周知的，但由于指定了专门设计的力矢量，因此这些示例与实际相关的示例有所不同。因此，我们在雷诺数1024处的两个空间维上提出了一个简单的稳态Navier-Stokes问题，这是一个十字形域中的碰撞流，其中详细研究了质量守恒性的不稳定性，并且没有规定力矢量。

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