Compact moving particle semi-implicit method for incompressible free-surface flow

Abstract

Recently, consistent meshfree particle methods have been intensively studied. It has been pointed out that numerical inaccuracy or instability could easily occur with incomplete or biased neighbor support. This study proposes a new meshfree particle method called the compact moving particle semi-implicit (CMPS) method to decrease the condition number. In the proposed CMPS, the first-order and second-order derivatives are discretized separately, enhancing the numerical stability significantly. By adopting a small dilation parameter of the compact support, the CMPS can remarkably improve accuracy and reduce computational costs. Formulations for zeroth-order, first-order, and second-order derivatives are derived, and various boundary conditions, e.g., Dirichlet and Neumann, are discussed. In order to better deal with complex free-surface flows using the CMPS, some new numerical techniques, i.e., optimized regularization and reconstructed particle shifting schemes, are also developed. Furthermore, the surface fitting method is extended to address the surface tension. A convergence study is conducted in complex geometry to verify the stability, accuracy, and efficiency of the CMPS. Then, second-order accuracy is confirmed using the Taylor–Green vortex problem. After that, numerical examples concerning various free-surface flows, including square patch, hydrostatic pressure, dam break, droplet oscillation, and droplet coalescence, are calculated to demonstrate the potential of the CMPS.