Iq-MPM

Abstract

We propose a novel scheme for simulating two-way coupled interactions between nonlinear elastic solids and incompressible fluids. The key ingredient of this approach is a ghost matrix operator-splitting scheme for strongly coupled nonlinear elastica and incompressible fluids through the weak form of their governing equations. This leads to a stable and efficient method handling large time steps under the CFL limit while using a single monolithic solve for the coupled pressure fields, even in the case with highly nonlinear elastic solids. The use of the Material Point Method (MPM) is essential in the designing of the scheme, it not only preserves discretization consistency with the hybrid Lagrangian-Eulerian fluid solver, but also works naturally with our novel interface quadrature (IQ) discretization for free-slip boundary conditions. While traditional MPM suffers from sticky numerical artifacts, our framework naturally supports discontinuous tangential velocities at the solid-fluid interface. Our IQ discretization results in an easy-to-implement, fully particle-based treatment of the interfacial boundary, avoiding the additional complexities associated with intermediate level set or explicit mesh representations. The efficacy of the proposed scheme is verified by various challenging simulations with fluid-elastica interactions.

MPMNet: A Data-Driven MPM Framework for Dynamic Fluid-Solid Interaction

“…Hu et al [40] presented the Moving Least Squares Material Point Method (MLS-MPM) that can handle coupling with rigid bodies and cutting, which MPM did not previously support. Fang et al [11] proposed an IQ-MPM algorithm for strong two-way coupling of incompressible fluids with volumetric elastic solids. Su et al [41] extended MPM for simulating various viscoelastic liquids with phase change.…”

“…Famous physics-based methods include particle-based method [1], grid-based method [2], hybrid grid/particle method [3], [4], [5], [6], [7]. Among them, Material Point Method (MPM) [8], a hybrid grid/particle method, attracts much attention in recent years since it has been successful in simulating many fluid-like materials, such as viscous liquid [9], incompressible liquid [10], [11], deformable [12] and fractured materials [13], [14], [15], with more complex and convincing fluidsolid dynamics.…”

“…interaction and motion towards fluid-solid coupling. Our fluid-solid coupling prediction is built upon Interface Quadrature Material Point Method (IQ-MPM)'s numerical solvers [11], inherits the advantages of grid-particle solvers that handle advection with accuracy and maintain incompressibility conditions. To break the bottleneck that restricts the time efficiency of the MPM method, we combine MPM and neural networks using a collaborative end-to-end structure for accelerated pressure solving.…”

A‐ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture

“…We also note the related works of [MSW * 09] for hair simulation, [SMT08] for cloth simulation, [NGL10] for sand simulation and [PAKF13] for bubble simulation, which bear similarities to MPM due to their hybrid nature. Various works have improved or modified aspects of the standard MPM techniques commonly used in graphics [FQL * 20, YSC * 18, XSH * 20, DHW * 19]. Among them, notably, Jiang et al [JSS * 15, JST17] proposed an Affine Particle‐In‐Cell (APIC) approach that conserves angular momentum and prevents visual artifacts such as noise, instability, clumping and volume loss/gain existing in both FLIP and PIC methods.…”

“…The Material Point Method (MPM) family of discretizations [SCS94], such as Fluid Implicit Particle (FLIP) [BKR88] and Particle‐in‐Cell (PIC) [SZS95], emerged as an effective choice for simulating various materials and gained popularity in visual effects (VFX) for providing high‐fidelity physics simulations of snow [SSC * 13], sand [KGP * 16, DBD16], phase change [SSJ * 14, GWW * 18], viscoelasticity [RGJ * 15, YSB * 15, SH * 21], viscoplasticity [FLGJ19], elastoplasticity [GTJS17], fluid structure interactions [FQL * 20], fracture [WFL * 19, HJST13], fluid‐sediment mixtures [TGK * 17, GPH * 18], baking and cooking [DHW * 19], and diffusion‐driven phenomena [XSH * 20]. In contrast to Lagrangian mesh‐based methods, such as the Finite Element Method (FEM) [ZTNZ77,SB12], and pure particle‐based methods, such as Smoothed Particle Hydrodynamics (SPH) [DG96, LLZ08], MPM merges the advantages of both Lagrangian and Eulerian approaches and automatically supports dynamic topology changes such as material splitting and merging.…”