Journal of Computational Physics
A fast adaptive vortex method in three dimensions
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
A node-centered local refinement algorithm for Poisson's equation in complex geometries
Journal of Computational Physics
A fourth-order accurate local refinement method for Poisson's equation
Journal of Computational Physics
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
A general fictitious domain method with immersed jumps and multilevel nested structured meshes
Journal of Computational Physics
A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
A Second-Order Accurate Conservative Front-Tracking Method in One Dimension
SIAM Journal on Scientific Computing
The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella [A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys. 147(2) (1998) 60-85] and extends work of McCorquodale, Colella and Johansen [A Cartesian grid embedded boundary method for the heat equation on irregular domains, J. Comput. Phys. 173 (2001) 620-635]. Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.