Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
SIAM Journal on Scientific Computing
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
Journal of Computational Physics
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
SIAM Review
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
Fast tree-based redistancing for level set computations
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A fast modular semi-Lagrangian method for moving interfaces
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering
Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering
An approach to local refinement of structured grids
Journal of Computational Physics
A novel dynamic load balancing scheme for parallel systems
Journal of Parallel and Distributed Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
A quadtree adaptive method for simulating fluid flows with moving interfaces
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
Journal of Computational Physics
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Sharp interface Cartesian grid methods are capable of simulating complex moving boundary problems on fixed meshes while treating embedded interfaces accurately. This article further enhances the effectiveness of the sharp interface method by devising techniques for adaptive mesh resolution combined with parallel processing. These extensions enable dealing with problems involving disparate length scales encountered in many applications. A tree-based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method for efficient and optimised calculations. Detailed timing and accuracy data are presented for a variety of benchmark problems involving moving boundaries. Guidelines for selecting mesh refinement criteria for moving boundary calculations are developed. Issues associated with parallelisation of the overall framework are tackled. The capabilities of the method are demonstrated in a number of moving boundary problems, which require adequate resolution of a wide range of length scales and three-dimensional flows.