Assessments of SIMPLE and ASIMPLE Algorithms Based on Buoyancy-Driven Cavity Flows

Authors : Jian Qin, Huachen Pan, Zefei Zhu, Xiaoqing Tian, and M. M. Rahman

Volume/Issue : Volume 5 - 2020, Issue 3 - March

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A comparative assessment between SIMPLE and artificial SIMPLE (ASIMPLE) algorithms is conducted based on two-dimensional buoyancy-driven incompressible cavity flows, using a cell-centered finitevolume formulation on a non-orthogonal collocated grid. Both methods are characteristically pressure-based; however, the ASIMPLE scheme additionally combines the concept of artificial compressibility with the pressure Poisson equation, provoking density perturbations that account for the transformation between primitive and conservative variables. An improved non-linear momentum interpolation scheme is employed at the cell face in discretizing the continuity equation, suppressing pressure oscillations effectively. A range of values is considered for the thermal Grashof number; excellent consistency is obtained between results available in the literature and numerical solutions adhering to both SIMPLE and ASIMPLE solvers. Numerical experiments in reference to buoyancy-driven cavity flows dictate that both contrivances (e.g., SIMPLE and ASIMPLE) 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 ASIMPLE method are the use of larger Courant numbers, enhanced robustness and convergence. Both procedures adopt an unfactored pseudo-time integration scheme and provide identical results.

Keywords : SIMPLE Algorithm, Artificial Compressibility, Sound Speed, Under-Relaxation (UR) Factor, Convergence and Robustness.


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