Implementation of Point-Implicit Diffusion Operator in a Moving-Particle Method (MPPM)

Abstract

A point-implicit strategy to circumvent the time-step constraint for diffusion process in a moving-particle method (MPPM) is proposed in this article. Since the Eulerian mesh has been established to deal with all pressure-related operators, it is also employed in constructing an accurate and effective local mesh (LM) formulation to represent the diffusion operator on the Lagranian particles. Explicit evaluation of the diffusion process will become inefficient due to the limited time step with a refined particle distribution. On the other hand, a fully implicit method requires an iterative procedure which will inevitably increase the computational burden. In the proposed point-implicit strategy, only the solution value at the objective particle is handled implicitly, and those at neighboring ones are treated explicitly. The time-step constraint on the diffusion process can then be taken out. All these efforts will result in an effective solution procedure for incompressible flow simulations.

Notes

Notes: ∗, scheme A; #, scheme B; %, convergence order; &, unstable solution.