Abstaining from a corrector step of SIMPLE-like algorithms, a coupled pressure-based algorithm is designed using a cell-centered finite-volume $\Delta$-approximation on a collocated grid to predict all-speed fluid flows. A consistently formulated cell-face dissipation scheme is invoked to unravel the occurrence of pressure–velocity decoupling. Modified Rusanov, Roe and Lax–Wendroff flux-difference schemes accompanied by a newly devised differentiable slope limiter function are used to compute inviscid fluxes over the entire spectrum of subsonic to hypersonic flow. Numerical experiments in reference to incompressible and compressible flows demonstrate that the proposed algorithm maintains an excellent consistency with analytic solutions and available literature data. The method is anticipated to be stable for an extensive range of Mach numbers with an avoidance of under-relaxation (UR) factors.

避免了类似SIMPLE算法的校正步骤，使用以单元为中心的有限体积设计了基于压力的耦合算法 $\Delta$-并置网格上的近似值以预测全速流体流动。调用一致制定的单元面耗散方案来揭示压力-速度解耦的发生。修改后的Rusanov，Roe和Lax–Wendroff通量差分方案，以及新设计的微分斜率限制器函数，可用于计算从亚音速到高音速流的整个频谱的无粘性通量。涉及不可压缩和可压缩流动的数值实验表明，该算法与解析解和现有文献数据保持了极好的一致性。预期该方法在广泛的马赫数范围内是稳定的，并且避免了欠松弛（UR）因子。