Abstract
A unified algorithm for compressible and incompressible flows is developed for Moving Particle Semi-implicit (MPS) method. Original MPS method was used for incompressible flows. MPS has been used to analyze complex flows, such as ship motion in ocean waves, droplet breakup and other complicate flows involving free surfaces, fluid breakup and coalescence. We extend MPS to manage compressible flows as well as incompressible flows in the same way as C-CUP (Cubic Interpolated Pseudo particle Combined Unified Procedure) method. We term it MPS-AS (MPS for All Speed) method. In MPS-AS method, compressible mass, momentum, energy conservation and gas state equations are used as governing equations. A Poisson equation is derived, using an evolution equation of pressure. This equation includes terms related to sound speed. These terms become prominent when a time step is small compared to sound speed. On the other hand, the discretized equation approaches MAC (Marker And Cell) method as the time step gets larger. The present algorithm can be applied to both incompressible and compressible flows including shock waves. Two-dimensional dam break and shock tube problems are solved. As a result, MPS-AS method can capture free surface (incompressible flow, dam break) and expansion wave, contact face and shock wave (compressible flow, shock tube).
