A class of higher order compact schemes for the unsteady two‐dimensional convection–diffusion equation with variable convection coefficients
A class of higher order compact schemes for the unsteady two‐dimensional convection–diffusion equation with variable convection coefficients
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DOI：
10.1002/fld.263
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发表时间：
2002-04
影响因子：
1.8
通讯作者：
J. C. Kalita;D. Dalal;A. K. Dass
中科院分区：
文献类型：
--
作者：
J. C. Kalita;D. Dalal;A. K. Dass
针对二维非定常变对流系数对流扩散方程，提出了一类带权时间离散的高阶紧致（HOC）格式.根据加权平均参数μ的选择，该格式在时间上具有二阶或更低的精度，在空间上具有四阶精度。对于0.5 μ π ι ~ 1，格式是无条件稳定的.与通常的HOC方案不同，这些方案能够使用网格纵横比而不是单位。它们有效地捕获了Dirichlet和Neumann边界条件下线性和非线性对流扩散方程的瞬态和稳态解。它们被应用于一个线性对流扩散问题和三个由二维不可压缩Navier-Stokes方程控制的不同复杂性的流动。所得结果与分析和建立的数值结果非常吻合。总体而言，该计划被认为是强大的，有效的和准确的。版权所有© 2002年约翰威利父子有限公司。
A class of higher order compact (HOC) schemes has been developed with weighted time discretization for the two‐dimensional unsteady convection–diffusion equation with variable convection coefficients. The schemes are second or lower order accurate in time depending on the choice of the weighted average parameter μ and fourth order accurate in space. For 0.5⩽μ⩽1, the schemes are unconditionally stable. Unlike usual HOC schemes, these schemes are capable of using a grid aspect ratio other than unity. They efficiently capture both transient and steady solutions of linear and nonlinear convection–diffusion equations with Dirichlet as well as Neumann boundary condition. They are applied to one linear convection–diffusion problem and three flows of varying complexities governed by the two‐dimensional incompressible Navier–Stokes equations. Results obtained are in excellent agreement with analytical and established numerical results. Overall the schemes are found to be robust, efficient and accurate. Copyright © 2002 John Wiley & Sons, Ltd.