Abstract The SIMPLE algorithm is devised by interpolating the mass continuity and non-advective momentum equations, provoking apparent simplicity and clarity in the formulation. The SIMPLE variant entitled as the SIMPLE-AC scheme convokes an artificial compressibility (AC) parameter to augment the diagonal dominance of discretized pressure-correction equation. Both methods are characteristically pressure-based, employing a cell-centered finite-volume Δ-formulation on a non-orthogonal collocated grid. A dual-dissipation scheme accompanied by limiting factors, repressing local extrema into the cell-face velocity and pressure, is used to unravel the issue of pressure-velocity decoupling; both SIMPLE and SIMPLE-AC schemes maintain an equivalent scaling (e.g., primary and auxiliary pseudo-time steps remain the same) with the cell-face dissipation and nodal influence coefficients. The phenomenal progress embedded in both contrivances facilitate an avoidance of the pervasive velocity/pressure under-relaxation. However, the SIMPLE-AC algorithm is benefited with using a higher CFL number, enhanced robustness, and convergence compared with the SIMPLE method.

中文翻译：

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避免 SIMPLE 算法中的欠松弛

摘要 SIMPLE 算法是通过插入质量连续性和非对流动量方程而设计的，在公式中引起明显的简单性和清晰度。被称为 SIMPLE-AC 方案的 SIMPLE 变体调用了一个人工可压缩性 (AC) 参数来增强离散压力校正方程的对角线优势。这两种方法的特点是基于压力，在非正交并置网格上采用以细胞为中心的有限体积 Δ 公式。双重消散方案伴随着限制因素，将局部极值抑制在细胞表面速度和压力中，用于解决压力-速度解耦问题；SIMPLE 和 SIMPLE-AC 方案都保持等效的缩放比例（例如，主要和辅助伪时间步保持不变）具有单元面耗散和节点影响系数。嵌入在这两种设计中的惊人进步有助于避免普遍存在的速度/压力松弛不足。然而，与 SIMPLE 方法相比，SIMPLE-AC 算法受益于使用更高的 CFL 数、增强的鲁棒性和收敛性。