An Energy Stable SPH Method for Incompressible Fluid Flow (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, a novel unconditionally energy stable Smoothed Particle Hydrodynamics (SPH) method is proposed and implemented for incompressible fluidflows. In this method, we apply operator splitting to break the momentum equationinto equations involving the non-pressure term and pressure term separately. The ideabehind the splitting is to simplify the calculation while still maintaining energy stability, and the resulted algorithm, a type of improved pressure correction scheme, isboth efficient and energy stable. We show in detail that energy stability is preservedat each full-time step, ensuring unconditionally numerical stability. Numerical examples are presented and compared to the analytical solutions, suggesting that the proposed method has better accuracy and stability. Moreover, we observe that if we areinterested in steady-state solutions only, our method has good performance as it canachieve the steady-state solutions rapidly and accurately.