Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
A coupled quadrilateral grid level set projection method applied to ink jet simulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An anelastic allspeed projection method for gravitationally stratified flows
Journal of Computational Physics
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Simulation of complex nonlinear elastic bodies using lattice deformers
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Journal of Computational Physics
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Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating time-dependent incompressible inviscid flow which combines a projection method with a "Cartesian grid" approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. The advection step is based on a Cartesian grid algorithm for compressible flow, in which the discretization of the body near the flow uses a volume-of-fluid representation. A redistribution procedure is used to eliminate time-step restrictions due to small cells where the boundary intersects the mesh. The projection step uses an approximate projection based on a Cartesian grid method for potential flow. The method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells. Convergence results are given for the projection itself and for the time-dependent algorithm in two dimensions. The method is also demonstrated on flow past a half-cylinder with vortex shedding.