2020/03/27 by S. Gagniere, Steven W. Gagniere, David A. B. Hyde +13 · 10 citations
Computer Science · Engineering · Physics and Astronomy · #Advection #Boundary (topology) #Computer Graphics and Visualization Techniques #Eulerian path #Flow (mathematics) #Fluid Dynamics and Heat Transfer #Grid #Interpolation (computer graphics) #Inviscid flow #Lattice Boltzmann Simulation Studies #Multilinear map #Projection (relational algebra) #Projection method #cs.CE #cs.GR #physics.comp-ph
paper · pdf · doi:10.1111/cgf.14096
published in Computer Graphics Forum 39(8), 1-14 (Wiley) · 13 pages, 18 figures
arxiv created 2020/03/27 · openalex created_date 2020/04/03 · openalex publication_date 2020/11/24 · arxiv updated 2021/02/09 · openalex updated_date 2026/08/05
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 C 1 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.