Stabilized mixed material point method for incompressible fluid flow analysis
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Author(s)
Chandra, Bodhinanda
Hashimoto, Ryota
Matsumi, Shinnosuke
Kamrin, Ken
Soga, Kenichi
Date Issued
February 2024
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Citation
Chandra, Bodhinanda, Hashimoto, Ryota, Matsumi, Shinnosuke, Kamrin, Ken and Soga, Kenichi. 2024. "Stabilized mixed material point method for incompressible fluid flow analysis." Computer Methods in Applied Mechanics and Engineering, 419.
Version
Final published version
Abstract
This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios.
Subjects
Computer Science Applications
General Physics and Astronomy
Mechanical Engineering
Mechanics of Materials
Computational Mechanics
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1016/j.cma.2023.116644
