A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Numerical analysis: mathematics of scientific computing
Numerical analysis: mathematics of scientific computing
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
The cost of balancing generalized quadtrees
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
SIAM Journal on Scientific Computing
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
A fast modular semi-Lagrangian method for moving interfaces
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Local-mesh, local-order, adaptive finite element methods with a-posteriori error estimators for elliptic partial differential equations
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
Journal of Computational Physics
Stability of approximate projection methods on cell-centered grids
Journal of Computational Physics
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
SIAM Journal on Scientific Computing
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Journal of Computational Physics
Journal of Scientific Computing
A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids
Journal of Scientific Computing
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
Hi-index | 31.49 |
We present an unconditionally stable second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive Cartesian grids. We employ quadtree and octree data structures as an efficient means to represent the grid. We use the supra-convergent Poisson solver of [C.-H. Min, F. Gibou, H. Ceniceros, A supra-convergent finite difference scheme for the variable coefficient Poisson equation on fully adaptive grids, CAM report 05-29, J. Comput. Phys. (in press)], a second order accurate semi-Lagrangian method to update the momentum equation, an unconditionally stable backward difference scheme to treat the diffusion term and a new method that guarantees the stability of the projection step on highly non-graded grids. We sample all the variables at the grid nodes, producing a scheme that is straightforward to implement. We propose two and three-dimensional examples to demonstrate second order accuracy for the velocity field and the divergence free condition in the L^1 and L^~ norms.