A dam-break simulation using the higher-order MPS(Moving Particle Semi-implicit) Method with a new treatment of the Neumann boundary condition

MPS(Moving Particle Semi-implicit) Method is a Lagrangian numerical analysis method, which does not necessary to set the lattice. Thus, it is effective for the analysis with complicated boundary such as free surface flow. On the other hand, since it is possible that particles varying their relative positions in MPS method, it courses a problem of non-uniformity in the spatial distribution of particles, thereby generating pressure fluctuation. Solving the pressure fluctuation problem has now been considered as the most important issue to improve the performance MPS method.

So far there are some ways been suggested to solve the problem, but the pressure fluctuation can not be erased fundamentally by any of those. To deal with the problem, Tamai, Koshizuka had proposed a higher-order accuracy differential model that can properly take into account the spatial arrangement of particles. However, this model has just been proposed 2013 and not been well verified when applied to simulation.

The present study has firstly comfirmed that compare to the old methods, Tamai, Koshizuka’s new model can solve the problem more effectively. Secondly, we try to use the new differential model to do the dam-break simulation which is a classical benchmark for free-surface issues. However, we found that the new model has problems when dealing with the Neumann boundary condition. So we proposed a new way of setting the Neumann boundary condition in order to use the new differential model correctly, and finially got a very good result in the simulation.