A high‐order accurate particle‐in‐cell method

Edwards, Essex; Bridson, Robert

doi:10.1002/nme.3356

Cited by 56 publications

(48 citation statements)

References 36 publications

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“…Note that for pure FLIP, the velocities are large on particle but zero when transferred to grid. [Zhu and Bridson 2005], including improved treatment of boundary conditions in irregular domains and coupling with rigid bodies [Batty et al 2007], viscosity treatment [Batty and Bridson 2008], Discontinuous-Galerkin-based adaptivity [Edwards and Bridson 2014], multiphase flow [Boyd and Bridson 2012] and higher-order accuracy [Edwards and Bridson 2012]. Notably, the approach of Edwards and Bridson in [Edwards and Bridson 2014] is similar to ours in that both can be seen to improve results by using more data per cell.…”

Section: Changesupporting

confidence: 62%

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The affine particle-in-cell method

et al. 2015

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Figure 1: APIC/PIC blends yield more energetic and more stable behavior than FLIP/PIC blends in a wine pour example. APIC/PIC blends are achieved analogously to FLIP/PIC in that it is a scaling of the particle affine matrices. c Disney. AbstractHybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particlein-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

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Section: Changesupporting

confidence: 62%

“…For similar reasons, Um et al develop a sub-grid-cell corrective forcing procedure to prevent particle bunching in [Um et al 2014]. Also, Edwards and Bridson add a regularization term to diminish particle noise not corrected by the grid [Edwards and Bridson 2012].…”

Section: Changementioning

confidence: 96%

The affine particle-in-cell method

et al. 2015

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“…We recognize that this error accumulation is the main drawback of the PIC scheme; however, we note that it can be minimized by choosing the Courant number carefully. A similar finding was alluded to, but not detailed, in the work of Edwards and Bridson regarding the error introduced by particle redistribution.…”

Section: Numerical Stability Error Accumulation and Order Of Convermentioning

confidence: 62%

“…If a fixed larger length of support is used, which involves more particles, Lagrange interpolation may fail since there will be no solution to the linear system . In this case, LS approximation can be used to achieve a high‐order transfer (see the work of Edwards and Bridson). The LS approximation looks for a polynomial p ( x ) to minimize the error

error = \sum_{p} {false(p false(x false) - f_{p} false)}^{2} .

The number of the particles within the compact support has to be greater or equal than the degrees of freedom of polynomial p ( x ).…”

Section: The High‐order Pic Methodsmentioning

confidence: 99%

A high‐order PIC method for advection‐dominated flow with application to shallow water waves

Wang

Kelly

2018

Numerical Methods in Fluids

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Summary A hybrid Eulerian‐Lagrangian particle‐in‐cell–type numerical method is developed for the solution of advection‐dominated flow problems. Particular attention is given over to the high‐order transfer of flow properties from the particles to the grid. For smooth flows, the method presented is of formal high‐order accuracy in space. The method is applied to solve the nonlinear shallow water equations resulting in a new, and novel, shock capturing shallow water solver. The approach is able to simulate complex shallow water flows, which can contain an arbitrary number of discontinuities. Both trivial and nontrivial bottom topography is considered, and it is shown that the new scheme is inherently well balanced, exactly satisfying the scriptC‐property. The scheme is verified against several one‐dimensional benchmark shallow water problems. These include cases that involve transcritical flow regimes, shock waves, and nontrivial bathymetry. In all the test cases presented, very good results are obtained.

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“…Nonuniform point distributions can pose problems for numerical methods that advect particles. Closest to our work is that of Edwards et al [2012], who pointed out that shearing flows can quickly introduce anisotropic point distributions for particle-in-cell methods, like MPM; they proposed a (non-conservative) method to resample points. Stomakhin et al [2014] also pointed to the need for a resampling technique for MPM as a direction for future work.…”

Section: Particle Models For Foams and Bubblesmentioning

confidence: 99%

Continuum Foam

et al. 2015

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We consider the simulation of dense foams composed of microscopic bubbles, such as shaving cream and whipped cream. We represent foam not as a collection of discrete bubbles, but instead as a continuum. We employ the Material Point Method (MPM) to discretize a hyperelastic constitutive relation augmented with the Herschel-Bulkley model of non-Newtonian viscoplastic flow, which is known to closely approximate foam behavior. Since large shearing flows in foam can produce poor distributions of material points, a typical MPM implementation can produce non-physical internal holes in the continuum. To address these artifacts, we introduce a particle resampling method for MPM. In addition, we introduce an explicit tearing model to prevent regions from shearing into artificially-thin, honey-like threads. We evaluate our method's efficacy by simulating a number of dense foams, and we validate our method by comparing to real-world footage of foam.

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A high‐order accurate particle‐in‐cell method

Cited by 56 publications

References 36 publications

The affine particle-in-cell method

The affine particle-in-cell method

A high‐order PIC method for advection‐dominated flow with application to shallow water waves

Continuum Foam

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