A conservative treatment of zonal boundaries for Euler equation calculations
Journal of Computational Physics
FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions
Journal of Computational Physics
A relaxation approach to patched-grid calculations with the Euler equations
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
On the use of composite grid schemes in computational aerodynamics
Computer Methods in Applied Mechanics and Engineering
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
A fully conservative interface algorithm for overlapped grids
Journal of Computational Physics
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
Animation and rendering of complex water surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
An efficient linearity-and-bound-preserving remapping method
Journal of Computational Physics
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Directable photorealistic liquids
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
On Multigrid for Overlapping Grids
SIAM Journal on Scientific Computing
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
Incompressible Navier-Stokes method with general hybrid meshes
Journal of Computational Physics
The repair paradigm: New algorithms and applications to compressible flow
Journal of Computational Physics
Journal of Computational Physics
Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow
Journal of Computational Physics
Computing a null divergence velocity field using smoothed particle hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
Journal of Computational Physics
Adaptive solution techniques for simulating underwater explosions and implosions
Journal of Computational Physics
Two-way coupling of fluids to rigid and deformable solids and shells
ACM SIGGRAPH 2008 papers
Two-Way Coupled SPH and Particle Level Set Fluid Simulation
IEEE Transactions on Visualization and Computer Graphics
Journal of Computational Physics
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Sharp interface immersed-boundary/level-set method for wave-body interactions
Journal of Computational Physics
A point-based method for animating incompressible flow
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A general topology Godunov method
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Matching fluid simulation elements to surface geometry and topology
ACM SIGGRAPH 2010 papers
Journal of Computational Physics
A symmetric positive definite formulation for monolithic fluid structure interaction
Journal of Computational Physics
Sources of spurious force oscillations from an immersed boundary method for moving-body problems
Journal of Computational Physics
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Journal of Computational Physics
A novel iterative direct-forcing immersed boundary method and its finite volume applications
Journal of Computational Physics
Journal of Computational Physics
A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions
Journal of Computational Physics
Journal of Computational Physics
Adaptive mesh, finite volume modeling of marine ice sheets
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.