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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >A novel and efficient approach to specifying Dirichlet far-field boundary condition of pressure Poisson equation
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A novel and efficient approach to specifying Dirichlet far-field boundary condition of pressure Poisson equation

机译：指定压力泊松方程Dirichlet远场边界条件的新颖有效方法

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Purpose - As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier-Stokes equation, the pressure variable is not incorporated in its solution procedure This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE. Design/methodology/approach - This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent The proposed approach is validated and assessed by a comparative study. Findings - This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation). Originality/value - The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems.
机译：目的-由于惩罚性单元内涡旋（pVIC）方法基于Navier-Stokes方程的涡度-速度形式，因此压力变量未包含在其求解过程中。这是基于涡度方法的优点之一如pVIC。但是，动态压力是工程问题中必不可少的流动特性。在pVIC中，可以通过速度和涡旋解通过压力泊松方程（PPE）明确评估压力场。因此，如何指定远场边界条件是一个重要的数值问题。因此，本文旨在稳健而准确地确定解决PPE的边界条件。设计/方法/方法-本文介绍了一种新的非迭代方法，用于指定Dirichlet远场边界条件以解决有界域中的PPE。使用从pVIC获得的速度和涡度场来计算压力场，并且压力的固体边界条件也由pVIC框架内的惩罚项强加。我们方法的基本思想是，由于保守矢量场的轮廓积分与路径无关，因此可以从闭合轮廓中的梯度场评估任意位置的压力。该方法已通过比较研究得到验证和评估。研究结果-这种非迭代方法已成功应用于2D和3D中基准问题的压力计算。该方法比其他所有经过测试的方法要快得多，而且不会影响准确性，并且即使对于使用小的计算域，无论源分布如何（泊松方程中的右侧），该方法都可以获得合理的压力场。独创性/价值-本文介绍的策略提供了一种有效的方法，用于指定压力Poisson问题在外域边界处的Dirichlet边界条件。与传统方法相比，它非常有效且坚固。所提出的想法也可以在处理无限域泊松问题的其他领域中采用。

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