Simulating liquids on dynamically warping grids

We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms

A practical octree liquid simulator with adaptive surface resolution

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2020/7-ART32 $15.00 https://doi.org/10.1145/3386569.3392460We propose a new adaptive liquid simulation framework that achieves highly detailed behavior with reduced implementation complexity. Prior work has shown that spatially adaptive grids are efficient for simulating large-scale liquid scenarios, but in order to enable adaptivity along the liquid surface these methods require either expensive boundary-conforming (re-)meshing or elaborate treatments for second order accurate interface conditions. This complexity greatly increases the difficulty of implementation and maintainability, potentially making it infeasible for practitioners. We therefore present new algorithms for adaptive simulation that are comparatively easy to implement yet efficiently yield high quality results. First, we develop a novel staggered octree Poisson discretization for free surfaces that is second order in pressure and gives smooth surface motions even across octree T-junctions, without a power/Voronoi diagram construction. We augment this discretization with an adaptivity-compatible surface tension force that likewise supports T-junctions. Second, we propose a moving least squares strategy for level set and velocity interpolation that requires minimal knowledge of the local tree structure while blending near-seamlessly with standard trilinear interpolation in uniform regions. Finally, to maximally exploit the flexibility of our new surface-adaptive solver, we propose several novel extensions to sizing function design that enhance its effectiveness and flexibility. We perform a range of rigorous numerical experiments to evaluate the reliability and limitations of our method, as well as demonstrating it on several complex high-resolution liquid animation scenarios.This research was supported by the JSPS Grant-in-Aid for Young Scientists (18K18060) and the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-04360-2014)

Efficient smoke simulation on curvilinear grids

This thesis present an efficient approach for performing smoke simulation on curvilinear grids. The solution of the Navier-Stokes equations on curvilinear is made on three steps: advection, pressure solving and velocity projection. The proposed advection method is simple, fast and unconditionally-stable. Our solution is able to maintain a staggered-grid variable arrangement, and includes an efficient solution to enforce mass conservation. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, lending to more realistic results, with just a small increment in computational cost. Moreover, we are able to condensate cells where interesting artifacts tend to appear, like swirling vortices or turbulence. We demonstrate the effectiveness of our approach, both in 2-D and 3-D, through a variety of high-quality smoke simulations and animations. These examples show the integration of our method with overlapping grids and multigrid techniques

Efficient smoke simulation on curvilinear grids

This thesis present an efficient approach for performing smoke simulation on curvilinear grids. The solution of the Navier-Stokes equations on curvilinear is made on three steps: advection, pressure solving and velocity projection. The proposed advection method is simple, fast and unconditionally-stable. Our solution is able to maintain a staggered-grid variable arrangement, and includes an efficient solution to enforce mass conservation. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, lending to more realistic results, with just a small increment in computational cost. Moreover, we are able to condensate cells where interesting artifacts tend to appear, like swirling vortices or turbulence. We demonstrate the effectiveness of our approach, both in 2-D and 3-D, through a variety of high-quality smoke simulations and animations. These examples show the integration of our method with overlapping grids and multigrid techniques