A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation
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Date
2020
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers' equation. We solve this equation using Newton's method enabled by C1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.
Description
@article{10.1111:cgf.14096,
journal = {Computer Graphics Forum},
title = {{A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation}},
author = {Gagniere, Steven and Hyde, David and Marquez-Razon, Alan and Jiang, Chenfanfu and Ge, Ziheng and Han, Xuchen and Guo, Qi and Teran, Joseph},
year = {2020},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14096}
}