Month: May 2024

Wei Li, Kui Wu, Mathieu Desbrun

Despite its visual appeal, the simulation of separated multiphase flows (i.e., streams of fluids separated by interfaces) faces numerous challenges in accurately reproducing complex behaviors such as guggling, wetting, or bubbling. These difficulties are especially pronounced for high Reynolds numbers and large density variations between fluids, most likely explaining why they have received comparatively little attention in Computer Graphics compared to single- or two-phase flows. In this paper, we present a full LBM solver for multifluid simulation. We derive a conservative phase field model with which the spatial presence of each fluid or phase is encoded to allow for the simulation of miscible, immiscible and even partially-miscible fluids, while the temporal evolution of the phases is performed using a D3Q7 lattice-Boltzmann discretization. The velocity field, handled through the recent high-order moment-encoded LBM (HOME-LBM) framework to minimize its memory footprint, is simulated via a velocity-based distribution stored on a D3Q27 or D3Q19 discretization to offer accuracy and stability to large density ratios even in turbulent scenarios, while coupling with the phases through pressure, viscosity, and interfacial forces is achieved by leveraging the diffuse encoding of interfaces. The resulting solver addresses a number of limitations of kinetic methods in both computational fluid dynamics and computer graphics: it offers a fast, accurate, and low-memory fluid solver enabling efficient turbulent multiphase simulations free of the typical oscillatory pressure behavior near boundaries. We present several numerical benchmarks, examples and comparisons of multiphase flows to demonstrate our solver’s visual complexity, accuracy, and realism.

Kinetic Simulation of Turbulent Multifluid Flows

Jiong Chen, Florian Schäfer, Mathieu Desbrun

The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. We show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves, up to four orders of magnitude in our series of tests.

Lightning-fast Method of Fundamental Solutions

• Lightning-Fast Method of Fundamental Solutions
• Kinetic Simulation of Turbulent Multifluid Flows
• Velocity-based Monte Carlo Fluids
• Neural Monte Carlo Fluid Simulation
• Going with the Flow
• VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality
• Differentiable solver for time-dependent deformation problems with contact
• Real-time Wing Deformation Simulation for Flying Insects
• Cyclogenesis: Simulating Hurricanes and Tornadoes
• Scintilla: Simulating Combustible Vegetation for Wildfires
• GIPC: Fast and stable Gauss-Newton optimization of IPC barrier energy
• Vertex Block Descent
• Primal-Dual Non-Smooth Friction for Rigid Body Animation
• Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes
• Modelling a Feather as a Strongly Anisotropic Elastic Shell
• Differentiable Voronoi Diagrams for Simulation of Cell-based Mechanical Systems
• Efficient Debris-flow Simulation for Steep Terrain Erosion
• An Induce-on-Boundary Magnetostatic Solver for Grid-based Ferrofluids
• A Vortex Particle-on-mesh Method for Soap Film Simulation
• Real-time Physically Guided Hair Interpolation
• Proxy Asset Generation for Cloth Simulation in Games
• A Dynamic Duo of Finite Elements and Material Points
• Lagrangian Covector Fluid With Free Surface
• Fluid Control With Laplacian Eigenfunctions
• Implicit Surface Tension for SPH Fluid Simulation
• A Dual-Particle Approach for Incompressible SPH Fluids
• Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps
• A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
• MERCI: Mixed curvature-based elements for computing equilibria of thin elastic ribbons
• Neural-assisted Homogenization of Yarn-level Cloth
• ContourCraft: Learning to Resolve Intersections in Neural Multi-garment Simulations
• Progressive Dynamics for Cloth and Shell Animation
• Super-resolution Cloth Animation With Spatial and Temporal Coherence
• Position-based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity
• Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton
• Simplicits: Mesh-free, Geometry-agnostic Elastic Simulation
• Efficient Position-based Deformable Colon Modeling for Endoscopic Procedures Simulation
• A Neural Network Model for Efficient Musculoskeletal-driven Skin Deformation
• Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity
• Contact Detection Between Curved Fibres: High Order Makes a Difference

Petros Tzathas, Boris Gailleton, Philippe Steer, Guillaume Cordonnier

Terrain generation methods have long been divided between procedural and physically-based. Procedural methods build upon the fast evaluation of a mathematical function but suffer from a lack of geological consistency, while physically-based simulation enforces this consistency at the cost of thousands of iterations unraveling the history of the landscape. In particular, the simulation of the competition between tectonic uplift and fluvial erosion expressed by the stream power law raised recent interest in computer graphics as this allows the generation and control of consistent large-scale mountain ranges, albeit at the cost of a lengthy simulation. In this paper, we explore the analytical solutions of the stream power law and propose a method that is both physically-based and procedural, allowing fast and consistent large-scale terrain generation. In our approach, time is no longer the stopping criterion of an iterative process but acts as the parameter of a mathematical function, a slider that controls the aging of the input terrain from a subtle erosion to the complete replacement by a fully formed mountain range. While analytical solutions have been proposed by the geomorphology community for the 1D case, extending them to a 2D heightmap proves challenging. We propose an efficient implementation of the analytical solutions with a multigrid accelerated iterative process and solutions to incorporate landslides and hillslope processes – two erosion factors that complement the stream power law.

Physically-based analytical erosion for fast terrain generation