A computational model of aquatic animal locomotion
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
A computational model of the cochlea using the immersed boundary method
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
The rapid evaluation of volume integrals of potential theory on general regions
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A fast Poisson solver for complex geometries
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
The blob projection method for immersed boundary problems
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A computational model of the cochlea using the immersed boundary method
A computational model of the cochlea using the immersed boundary method
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
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 pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
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
Journal of Computational Physics
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Dynamically coupled fluid-body interactions in vorticity-based numerical simulations
Journal of Computational Physics
Collision of multi-particle and general shape objects in a viscous fluid
Journal of Computational Physics
Journal of Computational Physics
Flux modelling in the finite-volume lattice Boltzmann approach
International Journal of Computational Fluid Dynamics
A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
Journal of Computational Physics
A conservative numerical method for the Cahn-Hilliard equation in complex domains
Journal of Computational Physics
Journal of Computational Physics
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
Hi-index | 31.58 |
We describe a method for solving the two-dimensional Navier-Stokes equations in irregular physical domains. Our method is based on an underlying uniform Cartesian grid and second-order finite-difference/finite-volume discretizations of the streamfunction-vorticity equations. Geometry representing stationary solid obstacles in the flow domain is embedded in the Cartesian grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells. Along the embedded boundary, we determine a distribution of vorticity sources needed to impose the no-slip flow conditions. This distribution appears as a right-hand-side term in the discretized fluid equations, and so we can use fast solvers to solve the linear systems that arise. To handle the advective terms, we use the high-resolution algorithms in CLAWPACK. We show that our Stokes solver is second-order accurate for steady state solutions and that our full Navier-Stokes solver is between first- and second-order accurate and reproduces results from well-studied benchmark problems in viscous fluid flow. Finally, we demonstrate the robustness of our code on flow in a complex domain.