Fast, adaptive summation of point forces in the two-dimensional Poisson equation
Journal of Computational Physics
A new vortex scheme for viscous flow
Journal of Computational Physics
A fast vortex method for computing 2D viscous flow
Journal of Computational Physics
Diffusing-vortex numerical scheme for solving incompressible Navier-Stokes equations
Journal of Computational Physics
An implementation of the fast multipole method without multipoles
SIAM Journal on Scientific and Statistical Computing
Fast triangulated vortex methods for the 2D Euler equations
Journal of Computational Physics
Boundary conditions for viscous vortex methods
Journal of Computational Physics
A fast adaptive vortex method in three dimensions
Journal of Computational Physics
An efficient implementation of particle methods for the incompressible Euler equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Resurrecting Core Spreading Vortex Methods: A New Scheme That Is Both Deterministic and Convergent
SIAM Journal on Scientific Computing
A new diffusion procedure for vortex methods
Journal of Computational Physics
Fast adaptive 2D vortex methods
Journal of Computational Physics
Merging Computational Elements in Vortex Simulations
SIAM Journal on Scientific Computing
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
Evaluation of the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements
SIAM Journal on Scientific Computing
A multi-moment vortex method for 2D viscous fluids
Journal of Computational Physics
Hi-index | 31.45 |
To simulate two-dimensional viscous incompressible flows based on a scheme of blob splitting and merging, we developed a vortex method and employed a fast multipole method to speed the computation of velocities. The diffusion of the vortex sheet induced at a solid wall by the no-slip boundary conditions is first modeled according to the analytical solution of Koumoutsakos and then converted into discrete blobs in the vicinity of the wall. To prevent the vorticity from entering the solid body, we introduce a concept residual circulation in a sense that only a partial circulation of the vortex sheet is diffused into the flow field; the rest remains at the wall. Blobs near the wall are thus avoided. Blobs near the wall that might cause large fluctuations in the strength of the vortex sheet are handled similarly. The solver thus developed requires no grid-based remeshing. We applied this solver to simulate the flow induced with an impulsively initiated circular cylinder; the results agree satisfactorily with those of previous experimental and numerical investigations.