Improvement of Accuracy and Stability of <scp>EMPS</scp> Method With a New Equation of State

ABSTRACT The explicit moving particle simulation (EMPS) method, due to its pressure calculation through the equation of state, has high computational efficiency and broad prospects for engineering applications. However, the conventional EMPS method has issues of numerical instability such as high‐frequency oscillations and discontinuous distributions of pressure. In this paper, to improve the accuracy and stability of numerical simulations, an enhanced δ MPS ‐EMPS method was proposed, in which a new enhanced equation of state and a diffusion term of particle number density were developed. The new enhanced equation of state includes the terms of the velocity divergence and the particle number density. It describes the relationship between pressure and fluid density through the changes in the velocity field and the particle number density field, resulting in a smooth pressure. It is worth noting that the artificial bulk modulus K in this equation is accurately calibrated using the specified pressure field calculated by the MPS method at the first time step. Additionally, the particle number density is corrected by introducing a diffusion term into the mass conservation equation. This approach can reduce high‐frequency pressure oscillations by filtering out non‐physical density fluctuations. The proposed method was evaluated and validated through simulations of four benchmark cases, including a hydrostatic pressure tank, the deformation of an elliptical droplet, the Taylor‐Green vortex flow, the 2D water dam‐break flow, and the evolution of a square patch of fluid. The simulation results proved the effectiveness and robustness of the enhanced δ MPS ‐EMPS method.