9.3.2 Central IRS on Unstructured Grids 非结构网格上的中心IRS[cfd-9-3-2]

在非结构网格上，CIRS通过把拉普拉斯算子（见式(5.24)）作用于残差来实现。于是，控制体 $$I$$ 内光顺后的残差 $\vec{R}^{*}_{I}$ 由如下隐式关系得到[14]en

CIRS is implemented on unstructured grids by applying the Laplacian operator (see Eq. (5.24)) to the residual. Thus, the smoothed residual $\vec{R}^{*}_{I}$ in a control volume $$I$$ is obtained from the implicit relation [14]

\vec{R}^{*}_{I} + \sum_{J=1}^{N_A}\epsilon\left(\vec{R}^{*}_{I} - \vec{R}^{*}_{J}\right) = \vec{R}_{I}\,. \tag{9.10}

求和遍及所有 $$N_A$$ 个相邻控制体。关系式(9.10)用Jacobi迭代对 $\vec{R}^{*}_{I}$ 求解。光顺系数的实用取值范围为 $0.5 \le \epsilon \le 0.8$ 。采用这些 $\epsilon$ 值，可以把CFL数（因而时间步长）提高二至五倍。由于矩阵对角占优，Jacobi迭代大约两步即收敛。en

The sum includes all $$N_A$$ adjacent control volumes. The relation (9.10) is solved for $\vec{R}^{*}_{I}$ using Jacobi iteration. Useful values of the smoothing coefficient are $0.5 \le \epsilon \le 0.8$ . With these values of $\epsilon$ it is possible to increase the CFL number (and hence the time step) two to five times. Due to the diagonal dominance of the matrix, the Jacobi iteration converges in about two steps.