Evaluation of a pressure splitting formulation for Weakly Compressible SPH: Fluid flow around periodic array of cylinders

In this paper, a pressure splitting formulation is proposed for Weakly Compressible SPH (WC-SPH) method and its capability in the suppression of the spurious oscillations is studied by conducting a stability analysis. The proposed formulation is implemented within the framework of a consistent SPH method. The predictions from the theoretical analysis are verified by the results of numerical test-cases. This method is applied to the incompressible fluid flow around periodic array of circular cylinders. The accuracy and the convergence of the results are investigated for benchmark problems. The results are also compared with those of the conventional WC-SPH method. In a similar test-case, the effects of the artificial speed of sound on the evolution of the transient solution and the occurrence of the spurious oscillations in the steady state are studied, and compared for both the conventional and the proposed WC-SPH formulations. The improvements in the evaluation of the pressure field, due to the proposed pressure splitting formulation, are shown for both a vanishing Reynolds number and a finite Reynolds number of Re∼O(1).