Dan Koschier, M.Sc.|
In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials.
In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell's polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.
We present a new method for particle based fluid simulation, using a combination of Projective Dynamics and Smoothed Particle Hydrodynamics (SPH). The Projective Dynamics framework allows the fast simulation of a wide range of constraints. It offers great stability through its implicit time integration scheme and is parallelizable in large parts, so that it can make use of modern multi core CPUs. Yet existing work only uses Projective Dynamics to simulate various kinds of soft bodies and cloth. We are the first ones to incorporate fluid simulation into the Projective Dynamics framework. Our proposed fluid constraints are derived from SPH and seamlessly integrate into the existing method. Furthermore, we adapt the solver to handle the constantly changing constraints that appear in fluid simulation. We employ a highly parallel matrix-free conjugate gradient solver, and thus do not require expensive matrix factorizations.
In this paper we introduce an efficient and stable implicit SPH method for the physically-based simulation of incompressible fluids. In the area of computer graphics the most efficient SPH approaches focus solely on the correction of the density error to prevent volume compression. However, the continuity equation for incompressible flow also demands a divergence-free velocity field which is neglected by most methods. Although a few methods consider velocity divergence, they are either slow or have a perceivable density fluctuation.
Our novel method uses an efficient combination of two pressure solvers which enforce low volume compression (below 0.01%) and a divergence-free velocity field. This can be seen as enforcing incompressibility both on position level and velocity level. The first part is essential for realistic physical behavior while the divergence-free state increases the stability significantly and reduces the number of solver iterations. Moreover, it allows larger time steps which yields a considerable performance gain since particle neighborhoods have to be updated less frequently. Therefore, our divergence-free SPH (DFSPH) approach is significantly faster and more stable than current state-of-the-art SPH methods for incompressible fluids. We demonstrate this in simulations with millions of fast moving particles.
We present a method for the adaptive simulation of brittle fracture of solid objects based on a novel reversible tetrahedral mesh refinement scheme. The refinement scheme preserves the quality of the input mesh to a large extent, it is solely based on topological operations, and does not alter the boundary, i.e. any geometric feature. Our fracture algorithm successively performs a stress analysis and increases the resolution of the input mesh in regions of high tensile stress. This results in an accurate location of crack origins without the need of a general high resolution mesh which would cause high computational costs throughout the whole simulation. A crack is initiated when the maximum tensile stress exceeds the material strength. The introduced algorithm then proceeds by iteratively recomputing the changed stress state and creating further cracks. Our approach can generate multiple cracks from a single impact but effectively avoids shattering artifacts. Once the tensile stress decreases, the mesh refinement is reversed to increase the performance of the simulation. We demonstrate that our adaptive method is robust, scalable and computes highly realistic fracture results.
We introduce a novel fast and robust simulation method for deformable solids that supports complex physical effects like lateral contraction, anisotropy or elastoplasticity. Our method uses a continuum-based formulation to compute strain and bending energies for two- and three-dimensional bodies. In contrast to previous work, we do not determine forces to reduce these potential energies, instead we use a position-based approach. This combination of a continuum-based formulation with a position-based method enables us to keep the simulation algorithm stable, fast and controllable while providing the ability to simulate complex physical phenomena lacking in former position-based approaches. We demonstrate how to simulate cloth and volumetric bodies with lateral contraction, bending, plasticity as well as anisotropy and proof robustness even in case of degenerate or inverted elements. Due to the continuous material model of our method further physical phenomena like fracture or viscoelasticity can be easily implemented using already existing approaches. Furthermore, a combination with other geometrically motivated methods is possible.