Unstructured Moving Particle Pressure Mesh (UMPPM) method for incompressible isothermal and non-isothermal flow computation

In this work, we intend to address the limitation of our earlier particle method, namely the Moving Particle Pressure Mesh (MPPM) method in handling arbitrary-shaped flow boundaries. The application of the Cartesian pressure mesh system adopted in our original MPPM method, which serves as the main key in recovering the divergence-free velocity condition for incompressible flow in the framework of particle method, is rather limited to rectangular flow domain. Here, the hybrid unstructured pressure mesh is adopted to remove the geometrical constraint of our earlier MPPM method. Coupled with the moving particle strategy in the Moving Particle Semi-implicit (MPS) method, the new method is named as the Unstructured Moving Particle Pressure Mesh (UMPPM) method in the current work. A consistent Laplacian model, namely the Consistent Particle Method (CPM) recently reported in the open literature is incorporated as well in the framework of UMPPM for discretizing the viscous term on the scattered particle cloud, while its implicit form is solved in the current work for overall robustness. Finally, we shall verify our UMPPM method with a series of benchmark solutions (for isothermal and non-isothermal flows) available from the literatures, including those obtained from the commercial code. It is appealing to find that the numerical solutions of UMPPM compare well with the benchmark solutions. In some cases, the accuracy of our UMPPM is better than that of the existing particle method such as Smoothed Particle Hydrodynamics (SPH).