Simulating free surface flow problems using hybrid particle element free Galerkin method

Abstract

A hybrid particle element free Galerkin (HPEFG) method is proposed for simulating free surface flow problems. The method combines the advantages of the element free Galerkin (EFG) method in the Eulerian description and particle method in the Lagrangian description, while overcoming the disadvantages of each. It makes the EFG method possible for solving problems of fluid flow with free surfaces and overcomes the difficulties in dealing with complex computational domains and mesh distortions. Two sets of nodes are independently placed in the computational domain for the HPEFG method. The nodes in one set used to represent fluid are called particles, and those in the other set used to compute flow variables are called EFG nodes. In order to test the validity and accuracy of the proposed meshfree method, four free surface flow problems are simulated and compared with other numerical results obtained by other numerical techniques, including the dam breaking, fluid–solid/fluid impacting and rotation of a square fluid patch. All the results show feasibility and ability of the proposed method to solve incompressible viscous fluid dynamic problems with moving free surface boundaries.