A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method

A higher order Laplacian model is proposed for enhancement and stabilization of pressure calculation by the MPS (Koshizuka S, Oka Y. Moving particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 1996;123:421–34) method. The higher order Laplacian is derived by taking the divergence of a particle-based gradient model (Monaghan, 1992) [18]. The proposed Higher order Laplacian is then applied for discretization of Laplacian of pressure and both Laplacian of pressure and that corresponding to the viscous forces in a previously improved MPS method, namely, the CMPS-HS (Khayyer and Gotoh, 2009) [8] method, resulting in CMPS-HS-HL-SV and CMPS-HS-HL-HV methods. A few numerical tests, namely, designed simple [8] and exponentially excited sinusoidal pressure oscillations and a violent sloshing flow (Kishev et al. 2006) [17] are carried out to demonstrate the enhancing and stabilizing effect of the proposed higher order Laplacian model.