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Explicit calculation for the pressure Poisson equation to simulate incompressible fluid flows in a mesh‐free method
Author(s) -
Xu Tibing
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.5022
Subject(s) - poisson's equation , compressibility , discretization , pressure gradient , mechanics , laplace operator , free surface , pressure correction method , mathematics , flow (mathematics) , computational fluid dynamics , mathematical analysis , physics
In this study, an equation is derived to explicitly solve the pressure Poisson equation (PPE) in the moving particle semiimplicit method. In the derivation, the PPE is discretized by an improved Laplacian model and the incompressible condition is satisfied by establishing a direct relationship between pressure and the known flow information. An improved gradient model is adopted in the method while a repulsive force is used to handle particle clustering. To validate the method, a hydrostatic problem, the impact of two rectangular fluid patches and dam‐breaking flows are simulated. The numerical results are compared with analytical solutions and experimental measurements in terms of free surface, pressure, and velocity. Good agreements in the comparisons are achieved, showing that the method can calculate smooth pressure field and accurate pressure and velocity distributions.