Modeling of Free Surface Flows Using Improved Material Point Method and Dynamic Adaptive Mesh Refinement

Abstract

The study uses the material point method (MPM) and dynamic adaptive mesh refinement (AMR) technique to simulate incompressible free surface flows. The MPM can be regarded as a quasi-meshless method in which the background grid acts like a scratch pad while the material point (hereafter referred to as particle) motion overlies it. The states of the particles are updated through the solutions on the background grid. The artificial compressibility coefficient is employed to treat incompressible flows as slightly compressible flows within the MPM framework. Boundary conditions, such as free surfaces and reflective walls (both slip and no-slip conditions), are implemented and tested using the ghost-cell method. A generalized far-field characteristic boundary for wave propagation simulation has been established. Typical water wave propagation and violent wave breaking involving discontinuous free surfaces are simulated as well as compared to the arbitrary Lagrangian-Eulerian (ALE) method. The results indicate that the improved material point method is a promising tool to simulate free surface flows.