Browsing by Author "Gagniere, Steven"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Gagniere, Steven; Hyde, David; Marquez-Razon, Alan; Jiang, Chenfanfu; Ge, Ziheng; Han, Xuchen; Guo, Qi; Teran, Joseph; Bender, Jan and Popa, Tiberiu
    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.
  • No Thumbnail Available
    Item
    A Linear and Angular Momentum Conserving Hybrid Particle/Grid Iteration for Volumetric Elastic Contact
    (ACM Association for Computing Machinery, 2023) Razon, Alan Marquez; Chen, Yizhou; Yushan, Han; Gagniere, Steven; Tupek, Michael; Teran, Joseph; Wang, Huamin; Ye, Yuting; Victor Zordan
    We present a momentum conserving hybrid particle/grid iteration for resolving volumetric elastic collision. Our hybrid method uses implicit time stepping with a Lagrangian finite element discretization of the volumetric elastic material together with impulse-based collision-correcting momentum updates designed to exactly conserve linear and angular momentum. We use a two-step process for collisions: first we use a novel gridbased approach that leverages the favorable collision resolution properties of Particle-In-Cell (PIC) techniques, then we finalize with a classical collision impulse strategy utilizing continuous collision detection. Our PIC approach uses Affine-Particle-In-Cell momentum transfers as collision preventing impulses together with novel perfectly momentum conserving boundary resampling and downsampling operators that prevent artifacts in portions of the boundary where the grid resolution is of disparate resolution. We combine this with a momentum conserving augury iteration to remove numerical cohesion and model sliding friction. Our collision strategy has the same continuous collision detection as traditional approaches, however our hybrid particle/grid iteration drastically reduces the number of iterations required. Lastly, we develop a novel symmetric positive semi-definite Rayleigh damping model that increases the convexity of the nonlinear systems associated with implicit time stepping. We demonstrate the robustness and efficiency of our approach in a number of collision intensive examples.