Improved Moving Particle Semi-implicit method for multiphase flow with discontinuity

The variation of physical properties across the interface and the inaccuracy of spatial derivative on discontinuity contribute to the numerical instability in multiphase flow with large density or viscosity ratio. With integral basic equation in Peridynamic theory under updated Lagrangian formulation and stress tensor calculation by Moving Particle Semi-implicit method(MPS), a new numerical approach on dealing with the abrupt physical quantities is introduced. Besides, a modified matrix inspired by the shape function in Peridynamics is added in the gradient and divergence operators to eliminate the error caused by irregular particle distribution. In addition, to decrease the calculation error caused by large properties difference, a decomposition process on the stress tensor and its divergence are proposed, the large acceleration difference by the discontinuity of density on the interface is smoothed after a mean density and the accuracy is validated by a simple example. Four benchmark cases, oscillating two-layer elliptical region, Rayleigh–Taylor instability, two-phase dam-break and bubble rising examples, are simulated to demonstrate the feasibility and accuracy of the proposed method in multiphase flow with both small and large physical quantity ratio.