Local pressure‐correction for the Navier‐Stokes equations,International Journal for Numerical Methods in Fluids

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Local pressure‐correction for the Navier‐Stokes equations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-10-07 , DOI: 10.1002/fld.4925
Utku Kaya ₁ , Roland Becker ₂ , Malte Braack ₁

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This article presents a novel local pressure correction method for incompressible fluid flows and documents a numerical study of this method. Pressure correction methods decouple the velocity and pressure components of the time‐dependent Navier‐Stokes equations and lead to a sequence of elliptic partial differential equations for both components instead of a saddle point problem. In some situations, the equations for the velocity components are solved explicitly (with time step restrictions) and thus the elliptic pressure problem remains to be the most expensive step. Here, we employ a multiscale procedure for the solution of the Poisson problem related to pressure. The procedure replaces the global Poisson problem by local Poisson problems on subregions. We propose a new Robin‐type boundary condition design for the local Poisson problems, which contains a coarse approximation of the global Poisson problem. Accordingly, no further communication between subregions is necessary and the method is perfectly adapted for parallel computations. Numerical experiments regarding a known analytical solution and flow around cylinder benchmarks show the effectivity of this new local pressure correction method.

中文翻译：

Navier-Stokes方程的局部压力校正

本文提出了一种针对不可压缩流体流动的新型局部压力校正方法，并对该方法进行了数值研究。压力校正方法将时间相关的Navier-Stokes方程的速度和压力分量解耦，并导致两个分量的椭圆偏微分方程序列，而不是鞍点问题。在某些情况下，速度分量的方程式已明确求解（有时间步长限制），因此椭圆压力问题仍然是最昂贵的步长。在这里，我们采用多尺度程序来解决与压力有关的泊松问题。该程序用子区域上的局部泊松问题代替了全局泊松问题。针对局部泊松问题，我们提出了一种新的Robin型边界条件设计，其中包含全局泊松问题的粗略近似。因此，不需要在子区域之间进行进一步的通信，并且该方法完全适合于并行计算。有关已知分析解决方案和绕汽缸基准流动的数值实验表明了这种新的局部压力校正方法的有效性。

更新日期：2020-10-07

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