A decoupled finite particle method for modeling incompressible flows with free surfaces

Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian particle method, and it has been applied to different areas in engineering and sciences. One concern of the conventional SPH is its low accuracy due to particle inconsistency, which hinders the further methodology development. The finite particle method (FPM) restores the particle consistency in the conventional SPH and thus significantly improves the computational accuracy. However, as pointwise corrective matrix inversion is necessary, FPM may encounter instability problems for highly disordered particle distribution. In this paper, through Taylor series analyses with integration approximation and assuming diagonal dominance of the resultant corrective matrix, a new meshfree particle approximation method, decoupled FPM (DFPM), is developed. DFPM is a corrective SPH method, and is flexible, cost-effective and easy in coding with better computational accuracy. It is very attractive for modeling problems with extremely disordered particle distribution as no matrix inversion is required. One- and two-dimensional numerical tests with different kernel functions, smoothing lengths and particle distributions are conducted. It is demonstrated that DFPM has much better accuracy than conventional SPH, while particle distribution and the selection of smoothing function and smoothing length have little influence on DFPM simulation results. DFPM is further applied to model incompressible flows including Poiseuille flow, Couette flow, shear cavity and liquid sloshing. It is shown that DFPM is as accurate as FPM while as flexible as SPH, and it is very attractive in modeling incompressible flows with possible free surfaces.