A fourth-order finite volume method with colocated variable arrangement
A fourth-order finite volume method with colocated variable arrangement
复制标题
共置变量排列的四阶有限体积法
DOI：
10.1016/0045-7930(94)00030-3
复制
发表时间：
1995
影响因子：
2.8
通讯作者：
M. Peric
中科院分区：
文献类型：
--
作者：
Ž. Lilek;M. Peric
提出了一种在直角坐标网格上四阶离散的二维Navier-Stokes方程和温度方程的有限体积法。该方法采用同位变量排列和SIMPLE型速度-压力耦合。的表面积分（对流和扩散通量通过控制体积面）近似辛普森的规则和多项式插值，和体积积分（源项）近似拟合四阶多项式通过九个点，并将其解析。应用于已知速度场的标量输运解以及盖驱动和浮力驱动的空腔流，与一阶和二阶格式相比，显示出上级精度。该方法可以很容易地扩展到控制体积的任意形状和非结构化网格。
A finite volume solution method for the two-dimensional Navier-Stokes equations and temperature equation with 4th order discretization on cartesian grids is presented. The method uses colocated variable arrangement and the SIMPLE-kind of velocity-pressure coupling. The surface integrals (convection and diffusion fluxes through control volume faces) are approximated by Simpson's rule and polynomial interpolation, and the volume integrals (source terms) are approximated by fitting a fourth-order polynomial through nine points and integrating it analytically. Applications to the solution of a scalar transport on a known velocity field and to the lid-driven and buoyancy-driven cavity flows show superior accuracy as compared to the first and second order schemes. The approach can be readily extended to control volumes of arbitrary shape and unstructured grids.