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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement
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A finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement

机译：具有非结构化扭曲网格的瞬态对流和扩散方程的有限体积公式及其在并置变量布置的流体流动模拟中的应用

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摘要

This paper describes a finite volume method for simulating transport processes governed by convection-diffusion type equations. The formulation is based on a cell-centred, unstructured grid. With an edge-based data structure, discretisation is independent of control volume (or cell) shape. By using a surface vector decomposition at the midpoint of the interface between cells, along with a deferred-correction approach, any cross-diffusion due to grid skewness can be readily accounted for when discretising the diffusive flux. For modelling fluid flow processes, a collocated arrangement of variables is employed so that a single coefficient matrix applies for the momentum equations of each velocity component. To avoid 'checkerboard oscillation' (arising from pressure-velocity decoupling) occurring under the collocated variable arrangement when a pressure-based solution algorithm is employed, a novel pseudo-flux interpolation method is proposed for unstructured grids, ensuring that the solution is both under-relaxation factor and time-step (for transient calculation) independent. The methodology can be formulated within a framework whereby either a coupled or a decoupled solution algorithm can be employed. The features and advantages of the method are demonstrated by solution of the Navier-Stokes equations for two benchmark flow problems.
机译：本文介绍了一种有限体积方法，用于模拟由对流扩散型方程控制的传输过程。该公式基于以单元为中心的非结构化网格。通过基于边缘的数据结构，离散化与控制体积（或像元）的形状无关。通过在单元格之间的界面的中点使用表面矢量分解以及延迟校正方法，可以在离散扩散通量时轻松解决由于网格偏斜导致的任何交叉扩散。为了对流体流动过程进行建模，采用变量的并置布置，以便单个系数矩阵适用于每个速度分量的动量方程。为避免在采用基于压力的求解算法时，在并置变量布置下发生“棋盘振荡”（由压力-速度解耦引起），针对非结构化网格，提出了一种新颖的伪磁通插值方法，确保求解都在松弛因子和时间步长（用于瞬态计算）无关。可以在框架内制定该方法，从而可以采用耦合或解耦的求解算法。通过解决两个基准流量问题的Navier-Stokes方程，证明了该方法的特点和优势。

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