A particle-grid superposition method for the Navier-Stokes equations
Journal of Computational Physics
Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations
SIAM Journal on Numerical Analysis
A new diffusion procedure for vortex methods
Journal of Computational Physics
Inviscid axisymmetrization of an elliptical vortex
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Vortex methods with spatially varying cores
Journal of Computational Physics
A general deterministic treatment of derivatives in particle methods
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
Scattered node compact finite difference-type formulas generated from radial basis functions
Journal of Computational Physics
Modified interpolation kernels for treating diffusion and remeshing in vortex methods
Journal of Computational Physics
An improved SPH method: Towards higher order convergence
Journal of Computational Physics
Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws
SIAM Journal on Numerical Analysis
Renormalized Meshfree Schemes II: Convergence for Scalar Conservation Laws
SIAM Journal on Numerical Analysis
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations
Journal of Computational Physics
Hi-index | 31.45 |
The general integral particle strength exchange (PSE) operators [J.D. Eldredge, A. Leonard, T. Colonius, J. Comput. Phys. 180 (2002) 686-709] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.