Abstract A comparative assessment between SIMPLE and its variant SIMPLE-C is conducted based on two-dimensional (2-D) incompressible flows, using a cell-centered finite-volume Δ -formulation on a collocated grid. The SIMPLE-C (SIMPLE Compressibility) scheme additionally combines the concept of artificial compressibility (AC) with the pressure Poisson equation, provoking the diagonal dominance of influence coefficients. An improved nonlinear momentum interpolation scheme is employed at the cell face in discretizing the continuity equation to suppress pressure oscillations. The pseudo-time step Δ t i remains the same in both schemes to conserve an analogous scaling with momentum and scalar nodal influence coefficients. Numerical experiments in reference to buoyancy-driven cavity flow dictate that both contrivances execute a residual smoothing enhancement, facilitating an avoidance of the velocity/pressure under-relaxation (UR). However, compared with the SIMPLE approach, included benefits of the SIMPLE-C method are the use of larger Courant numbers, enhanced robustness and convergence. Excellent consistency is obtained between results available in the literature and numerical solutions obtained by both SIMPLE and SIMPLE-C solvers. The segregated SIMPLE algorithm is finally reformulated in conjunction with a new slope/flux limiter function to predict fluid flow at all speeds. Numerical results show that the compressible variant of SIMPLE replicates correct shock speed, well-resolved shock front, contact discontinuity and rarefaction waves when compared with analytical solutions. Compressible laminar flows are computed to further support the accuracy and robustness of proposed algorithm.

中文翻译：

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使用 SIMPLE 算法引入可压缩性

摘要 基于二维 (2-D) 不可压缩流，在并置网格上使用以单元为中心的有限体积 Δ 公式，对 SIMPLE 及其变体 SIMPLE-C 进行了比较评估。SIMPLE-C（SIMPLE Compressibility）方案另外将人工压缩性（AC）的概念与压力泊松方程相结合，激发了影响系数的对角优势。在单元面采用改进的非线性动量插值方案来离散连续性方程以抑制压力振荡。伪时间步长 Δ ti 在两种方案中保持相同，以保存具有动量和标量节点影响系数的类似缩放。参考浮力驱动的腔流的数值实验表明，这两种设计都执行残余平滑增强，有助于避免速度/压力欠松弛 (UR)。然而，与 SIMPLE 方法相比，SIMPLE-C 方法的优点包括使用更大的 Courant 数、增强的鲁棒性和收敛性。文献中可用的结果与 SIMPLE 和 SIMPLE-C 求解器获得的数值解之间获得了极好的一致性。分离的 SIMPLE 算法最终结合新的斜率/通量限制器功能重新制定，以预测所有速度下的流体流动。数值结果表明，SIMPLE 的可压缩变体复制了正确的激波速度、解析良好的激波前沿、与解析解相比，接触不连续性和稀疏波。计算可压缩层流以进一步支持所提出算法的准确性和鲁棒性。