A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains
Journal of Computational Physics
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
Handbook of mathematics (3rd ed.)
Handbook of mathematics (3rd ed.)
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
Multiphase dynamics in arbitrary geometries on fixed Cartesian grids
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
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
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
Journal of Computational Physics
Derivation and validation of a novel implicit second-order accurate immersed boundary method
Journal of Computational Physics
International Journal of Computational Fluid Dynamics
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
A conservative immersed interface method for Large-Eddy Simulation of incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Link-wise artificial compressibility method
Journal of Computational Physics
Stability investigation of a difference scheme for incompressible Navier-Stokes equations
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
An accurate moving boundary formulation in cut-cell methods
Journal of Computational Physics
Journal of Computational Physics
Advances in Engineering Software
Hi-index | 31.52 |
A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel "cell-linking" method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re = 40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow.