Stabilized LSMPS method for complex free-surface flow simulation

Abstract

In this study, a new quasi-Lagrangian particle method is developed aiming at accurate and stable numerical simulation of complex free-surface flows. The main novelties of this development are the free-surface treatment using surface fitting and the new discretization schemes. By using linear surface fitting, the normal vector and the signed distance to the free surface are accurately and stably obtained. The existing consistent spatial discretization scheme, namely, the LSMPS scheme, is extended by adopting regularized least squares, diffuse derivative constraints, and constrained least squares. Based on this scheme, new formulations are proposed particularly for the pressure Poisson equation and the pressure gradient operator. By using a Taylor–Green vortex problem, 2nd-order accuracy in space is confirmed for the 2nd-order discretization scheme. Furthermore, highly accurate solutions are obtained for various test cases, including free-surface deformations of moderate to high complexity. Thus, the proposed method is indicated to have high accuracy and stability for complex free-surface flow simulations.