An Efficient Solver for Two‐way Coupling Rigid Bodies with Incompressible Flow

We present an efficient solver for monolithic two‐way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low‐dimensional nature of the solid equations. We observe that a single Multigrid V‐cycle for the fluid equations serves as a very effective preconditioner for solving the Schur‐complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly‐free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two‐way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation.     

Accelerating Liquid Simulation With an Improved Data-Driven Method

In physics-based liquid simulation for graphics applications, pressure projection consumes a significant amount of computational time and is frequently the bottleneck of the computational efficiency. How to rapidly apply the pressure projection and at the same time how to accurately capture the liquid geometry are always among the most popular topics in the current research trend in liquid simulations. In this paper, we incorporate an artificial neural network into the simulation pipeline for handling the tricky projection step for liquid animation. Compared with the previous neural-network-based works for gas flows, this paper advocates new advances in the composition of representative features as well as the loss functions in order to facilitate fluid simulation with free-surface boundary. Specifically, we choose both the velocity and the level-set function as the additional representation of the fluid states, which allows not only the motion but also the boundary position to be considered in the neural network solver. Meanwhile, we use the divergence error in the loss function to further emulate the lifelike behaviours of liquid. With these arrangements, our method could greatly accelerate the pressure projection step in liquid simulation, while maintaining fairly convincing visual results. Additionally, our neutral network performs well when being applied to new scene synthesis even with varied boundaries or scales.     

Direct Position‐Based Solver for Stiff Rods

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.     

An Efficient Hybrid Incompressible SPH Solver with Interface Handling for Boundary Conditions

We propose a hybrid smoothed particle hydrodynamics solver for efficientlysimulating incompressible fluids using an interface handling method for boundary conditions in the pressure Poisson equation. We blend particle density computed with one smooth and one spiky kernel to improve the robustness against both fluid–fluid and fluid–solid collisions. To further improve the robustness and efficiency, we present a new interface handling method consisting of two components: free surface handling for Dirichlet boundary conditions and solid boundary handling for Neumann boundary conditions. Our free surface handling appropriately determines particles for Dirichlet boundary conditions using Jacobi‐based pressure prediction while our solid boundary handling introduces a new term to ensure the solvability of the linear system. We demonstrate that our method outperforms the state‐of‐the‐art particle‐based fluid solvers.     

Detailed Rigid Body Simulation with Extended Position Based Dynamics

We present a rigid body simulation method that can resolve small temporal and spatial details by using a quasi explicit integration scheme that is unconditionally stable. Traditional rigid body simulators linearize constraints because they operate on the velocity level or solve the equations of motion implicitly thereby freezing the constraint directions for multiple iterations. Our method always works with the most recent constraint directions. This allows us to trace high speed motion of objects colliding against curved geometry, to reduce the number of constraints, to increase the robustness of the simulation, and to simplify the formulation of the solver. In this paper we provide all the details to implement a fully fledged rigid body solver that handles contacts, a variety of joint types and the interaction with soft objects.     

Robust and Efficient Wave Simulations on Deforming Meshes

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.     

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.     

DYVERSO: A Versatile Multi‐Phase Position‐Based Fluids Solution for VFX

Many impressive fluid simulation methods have been presented in research papers before. These papers typically focus on demonstrating particular innovative features, but they do not meet in a comprehensive manner the production demands of actual VFX pipelines. VFX artists seek methods that are flexible, efficient, robust and scalable, and these goals often conflict with each other. In this paper, we present a multi‐phase particle‐based fluid simulation framework, based on the well‐known Position‐Based Fluids (PBF) method, designed to address VFX production demands. Our simulation framework handles multi‐phase interactions robustly thanks to a modified constraint formulation for density contrast PBF. And, it also supports the interaction of fluids sampled at different resolutions. We put special care on data structure design and implementation details. Our framework highlights cache‐efficient GPU‐friendly data structures, an improved spatial voxelization technique based on Z‐index sorting, tuned‐up simulation algorithms and two‐way‐coupled collision handling based on VDB fields. Altogether, our fluid simulation framework empowers artists with the efficiency, scalability and versatility needed for simulating very diverse scenes and effects.     

A Multilevel SPH Solver with Unified Solid Boundary Handling

We propose a geometric multilevel solver for efficiently solving linear systems arising from particle‐based methods. To apply this method to particle systems, we construct the hierarchy, establish the correspondence between solutions at the particle and grid levels, and coarsen simulation elements taking boundary conditions into account. In addition, we propose a new solid boundary handling method to solve a pressure Poisson equation in a unified manner. We demonstrate that our method can handle general fluid simulation scenarios including two‐way fluid‐solid coupling, and the computational cost of this new solver scales nearly linearly with respect to the number of unknowns, unlike previous solvers for particle‐based methods.     

Primal/Dual Descent Methods for Dynamics

We examine the relationship between primal, or force-based, and dual, or constraint-based formulations of dynamics. Variational frameworks such as Projective Dynamics have proved popular for deformable simulation, however they have not been adopted for contact-rich scenarios such as rigid body simulation. We propose a new preconditioned frictional contact solver that is compatible with existing primal optimization methods, and competitive with complementarity-based approaches. Our relaxed primal model generates improved contact force distributions when compared to dual methods, and has the advantage of being differentiable, making it well-suited for trajectory optimization. We derive both primal and dual methods from a common variational point of view, and present a comprehensive numerical analysis of both methods with respect to conditioning. We demonstrate our method on scenarios including rigid body contact, deformable simulation, and robotic manipulation.     

A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

     

Stable and Fast Fluid–Solid Coupling for Incompressible SPH

The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum‐conserving velocity‐position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid–solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two‐way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios.     

Multi-agent Path Planning with Heterogenous Interactions in Tight Spaces

By starting with the assumption that motion is fundamentally a decision making problem, we use the world-line concept from Special Relativity as the inspiration for a novel multi-agent path planning method. We have identified a particular set of problems that have so far been overlooked by previous works. We present our solution for the global path planning problem for each agent and ensure smooth local collision avoidance for each pair of agents in the scene. We accomplish this by modelling the collision-free trajectories of the agents through 2D space and time as rods in 3D. We obtain smooth trajectories by solving a non-linear optimization problem with a quasi-Newton interior point solver, initializing the solver with a non-intersecting configuration from a modified Dijkstra's algorithm. This space–time formulation allows us to simulate previously ignored phenomena such as highly heterogeneous interactions in very constrained environments. It also provides a solution for scenes with unnaturally symmetric agent alignments without the need for jittering agent positions or velocities.     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

Aggregation and clogging phenomena of rigid microparticles in microfluidics

We developed a numerical tool to investigate the phenomena of aggregation and clogging of rigid microparticles suspended in a Newtonian fluid transported through a straight microchannel. In a first step, we implement a time-dependent one-way coupling Discrete Element Method (DEM) technique to simulate the movement and effect of adhesion on rigid microparticles in two- and three-dimensional computational domains. The Johnson–Kendall–Roberts (JKR) theory of adhesion is applied to investigate the contact mechanics of particle–particle and particle–wall interactions. Using the one-way coupled solver, the agglomeration, aggregation and deposition behavior of the microparticles is studied by varying the Reynolds number and the particle adhesion. In a second step, we apply a two-way coupling CFD–DEM approach, which solves the equation of motion for each particle, and transfers the force field corresponding to particle–fluid interactions to the CFD toolbox OpenFOAM. Results for the one-way (DEM) and two-way (CFD–DEM) coupling techniques are compared in terms of aggregate size, aggregate percentages, spatial and temporal evaluation of aggregates in 2D and 3D. We conclude that two-way coupling is the more realistic approach, which can accurately capture the particle–fluid dynamics in microfluidic applications.     

Coupling multibody dynamics and computational fluid dynamics on 8192 processor cores

This paper describes a method for the fully resolved simulation of particle laden flows. For this purpose, we discuss the parallelization of large scale coupled fluid structure interaction with up to 37 million geometrically modeled moving objects incorporated in the flow. The simulation is performed using a 3D lattice Boltzmann solver for the fluid flow and a so-called rigid body physics engine for the treatment of the objects. The numerical algorithms and the parallelization are discussed in detail. Furthermore, performance results are presented for test cases on up to 8192 processor cores running on an SGI Altix supercomputer. The approach enables a detailed simulation of large scale particulate flows that are relevant for many industrial applications.     

Detail‐Preserving Explicit Mesh Projection and Topology Matching for Particle‐Based Fluids

We propose a new explicit surface tracking approach for particle‐based fluid simulations. Our goal is to advect and update a highly detailed surface, while only computing a coarse simulation. Current explicit surface methods lose surface details when projecting on the isosurface of an implicit function built from particles. Our approach uses a detail‐preserving projection, based on a signed distance field, to prevent the divergence of the explicit surface without losing its initial details. Furthermore, we introduce a novel topology matching stage that corrects the topology of the explicit surface based on the topology of an implicit function. To that end, we introduce an optimization approach to update our explicit mesh signed distance field before remeshing. Our approach is successfully used to preserve the surface details of melting and highly viscous objects, and shown to be stable by handling complex cases involving multiple topological changes. Compared to the computation of a high‐resolution simulation, using our approach with a coarse fluid simulation significantly reduces the computation time and improves the quality of the resulting surface.     

Implicit Contact Handling for Deformable Objects

We present an algorithm for robust and efficient contact handling of deformable objects. By being aware of the internal dynamics of the colliding objects, our algorithm provides smooth rolling and sliding, stable stacking, robust impact handling, and seamless coupling of heterogeneous objects, all in a unified manner. We achieve dynamicsawareness through a constrained dynamics formulation with implicit complementarity constraints, and we present two major contributions that enable an efficient solution of the constrained dynamics problem: a time stepping algorithm that robustly ensures non-penetration and progressively refines the formulation of constrained dynamics, and a new solver for large mixed linear complementarity problems, based on iterative constraint anticipation. We show the application of our algorithm in challenging scenarios such as multi-layered cloth moving at high velocities, or colliding deformable solids simulated with large time steps.     

Accelerated numerical simulations of a heaving floating body by coupling a motion solver with a two-phase fluid solver

This paper presents a study on the coupling between a fluid solver and a motion solver to perform fluid–structure interaction (FSI) simulations of floating bodies such as point absorber wave energy converters heaving under wave loading. The two-phase fluid solver with dynamic mesh handling, interDyMFoam, is a part of the Computational Fluid Dynamics (CFD) toolbox OpenFOAM. The incompressible Navier–Stokes (NS) equations are solved together with a conservation equation for the Volume of Fluid (VoF). The motion solver is computing the kinematic body motion induced by the fluid flow. A coupling algorithm is needed between the fluid solver and the motion solver to obtain a converged solution between the hydrodynamic flow field around and the kinematic motion of the body during each time step in the transient simulation. For body geometries with a significant added mass effect, simple coupling algorithms show slow convergence or even instabilities. In this paper, we identify the mechanism for the numerical instability and we derive an accelerated coupling algorithm (based on a Jacobian) to enhance the convergence speed between the fluid and motion solver. Secondly, we illustrate the coupling algorithm by presenting a free decay test of a heaving wave energy converter. Thirdly and most challenging, a water impact test of a free falling wedge with a significant added mass effect is successfully simulated. For both test cases, the numerical results obtained by using the accelerated coupling algorithm are in a very good agreement with the experimental measurements.