A momentum-conserving implicit material point method for surface tension with contact angles and spatial gradients

Chen, Jingyu; Kala, Victoria; Marquez-Razon, Alan; Gueidon, Elias; Hyde, David; Teran, Joseph

doi:10.1145/3450626.3459874

Cited by 13 publications

(7 citation statements)

References 92 publications

(115 reference statements)

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“…al. [48] modelled the surface tension with a momentum conserving implicit MPM. In their method, two different surface tension coefficients were used for a liquid drop to distinguish the liquid-gas and liquidsolid interfaces of a droplet on a surface.…”

Section: Materials Point Methodsmentioning

confidence: 99%

“…al. [48] assumed that the surface tension coefficient between solid-gas is zero with a free-surface assumption, then the solid-liquid contact angle can be estimated by −𝛾𝛾 𝑠𝑠𝑙𝑙 𝛾𝛾 𝑙𝑙𝑙𝑙 ⁄ according to equation (1). Different contact angles can be produced by using different surface tension coefficients between solid-liquid and liquid-gas interfaces.…”

Section: Contact Anglementioning

confidence: 99%

“…Combines the features of mesh methods and particle methods Validation is needed Droplet dynamics with smoothed surfaces [48,67] As a mesh-based method, one notable aspect about VOF is its high computational accuracy. However, the accuracy of VOF is dependent on the quality of the mesh, and its use on complex interfaces is inconvenient.…”

Section: Mpmmentioning

confidence: 99%

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Modelling of water droplet dynamics on hydrophobic soils: a review

Zhang

Lourenço

2023

E3S Web of Conf.

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The hydrophobicity of soils (or soil water repellency) can be naturally promoted by wildfires or synthetically induced by hydrophobic compounds (polydimethylsiloxane, tong oil, etc.). Soil phenomena can be related to hydrophobicity, such as soil erosion (splash erosion and rill erosion) and post-wildfire debris flows. The hydrophobicity of soils is characterized by the contact angle, and the interactions between water droplet and solid particles including spreading, oscillation, and infiltration. Early studies on soil water repellency mainly focus on the experimental aspects, while with the development of advanced numerical tools, numerical methods have been widely applied to study the hydraulic properties of hydrophobic granular materials in recent years. This paper comprehensively investigates the different numerical methods for modelling the interaction between water droplets and hydrophobic soils, i.e., smoothed particle hydrodynamics (SPH), lattice Boltzmann method (LBM), material point method (MPM), and volume of fluid (VOF). The features of different method are summarized, and the future work are discussed.

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Section: Materials Point Methodsmentioning

confidence: 99%

Section: Contact Anglementioning

confidence: 99%

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Modelling of water droplet dynamics on hydrophobic soils: a review

Zhang

Lourenço

2023

E3S Web of Conf.

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“…MPM was first introduced into computer graphics by 9 to simulate snow. Due to its excellent physical accuracy and natural support for topology changes, MPM has been extensively applied to simulate various phenomena including sand 21 , lava 22 , viscoelastic/viscoplastic foam 23,24 , cloth 25 , fracture 10,26,11 , magnetized material 27 , multi-species coupling 28,4,3 , even hydrophobicity and hydrophilicity 29 . In order to address the significant numerical dissipation in MPM, affine particle-in-cell (APIC) 30 incorporated a local velocity gradient to preserve the momentum of particles, and Fei et al 31 further improved it with several advection strategies.…”

Section: Materials Point Methodsmentioning

confidence: 99%

MPM-driven Dynamic Desiccation Cracking and Curling in Unsaturated Soils

Chen

et al. 2023

Preprint

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Desiccation cracking of soil-like materials is a common phenomenon in natural dry environment, however, it remains a challenge to model and simulate complicated multi-physical processes inside the porous structure. With the goal of tracking such physical evolution accurately, we propose an MPM based method to simulate volumetric shrinkage and crack during moisture diffusion. At the physical level, we introduce Richards equations to evolve the dynamic moisture field to model evaporation and diffusion in unsaturated soils, with which a elastoplastic model is established to simulate strength changes and volumetric shrinkage via a novel saturation-based hardening strategy during plastic treatment. At the algorithmic level, we develop an MPM-fashion numerical solver for the proposed physical model and achieve stable yet efficient simulation towards delicate deformation and fracture. At the geometric level, we propose a correlating stretching criteria and a saturation-aware extrapolation scheme to extend existing surface reconstruction for MPM, producing visual compelling soil appearance. Finally, we manifest realistic simulation results based on the proposed method with several challenging scenarios, which demonstrates usability and efficiency of our method.

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“…The solution of large, sparse systems of linear equations is ubiquitous when partial differential equations (PDEs) are discretized to simulate complex natural phenomena such as fluid flow [29], thermodynamics [8], mechanical fracture [36], etc. Discretization often leads to a linear system…”

Section: Introductionmentioning

confidence: 99%

A Deep Gradient Correction Method for Iteratively Solving Linear Systems

Kaneda¹,

Osman²,

Chen³

et al. 2022

Preprint

Self Cite

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We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L 2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-ofthe-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.Preprint. Under review.

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A momentum-conserving implicit material point method for surface tension with contact angles and spatial gradients

Cited by 13 publications

References 92 publications

Modelling of water droplet dynamics on hydrophobic soils: a review

Modelling of water droplet dynamics on hydrophobic soils: a review

MPM-driven Dynamic Desiccation Cracking and Curling in Unsaturated Soils

A Deep Gradient Correction Method for Iteratively Solving Linear Systems

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