Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder
Journal of Computational Physics
A higher-order boundary treatment for Cartesian-Grid method
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
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
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
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
Journal of Computational Physics
HyPAM: A hybrid continuum-particle model for incompressible free-surface flows
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
Journal of Computational Physics
Nested Cartesian grid method in incompressible viscous fluid flow
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
An immersed boundary method for the incompressible Navier-Stokes equations in irregular domains is developed using a local ghost cell approach. This method extends the solution smoothly across the boundary in the same direction as the discretization it will be used for. The ghost cell value is determined locally for each irregular grid cell, making it possible to treat both sharp corners and thin plates accurately. The time stepping is done explicitly using a second order Runge-Kutta method. The spatial derivatives are approximated by finite difference methods on a staggered, Cartesian grid with local grid refinements near the immersed boundary. The WENO scheme is used to treat the convective terms, while all other terms are discretized with central schemes. It is demonstrated that the spatial accuracy of the present numerical method is second order. Further, the method is tested and validated for a number of problems including uniform flow past a circular cylinder, impulsively started flow past a circular cylinder and a flat plate, and planar oscillatory flow past a circular cylinder and objects with sharp corners, such as a facing square and a chamfered plate.