PhD Candidate, Bodhinanda Chandra, Prof. Kenichi Soga, and collaborators from Kyoto University, Hiroshima University, and MIT recently published a paper in Computer Methods in Applied Mechanics and Engineering, entitled “Stabilized mixed material point method for incompressible fluid flow analysis” (https://doi.org/10.1016/j.cma.2023.116644). In the proposed work, a stabilized mixed material point method (MPM) formulation is developed to simulate a stable and accurate simulation of incompressible fluid flows. The developed formulation employed a nonlinear-implicit time integration with mixed displacement-pressure field as the primary variables. Here, to satisfy the discrete inf-sup condition, the variational multiscale (VMS) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are adopted for the MPM formulation. Furthermore, numerical accuracy and stability are enhanced by mitigating quadrature and transfer errors. Several numerical examples are investigated to assess the accuracy and demonstrate the capability of the proposed mixed MPM approach in simulating different complex computational fluid dynamics (CFD) problems.
A video highlighting the work on the lid-driven cavity problem and dam-break flow is shown below.
2D Lid-driven cavity problem comparing the fractional-step approach and the proposed mixed MPM with PSPG and VMS stabilization. The FLIP and TPIC transfer schemes are utilized as indicated by the first and second rows.