Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations
SIAM Journal on Numerical Analysis
Boundary conditions for viscous vortex methods
Journal of Computational Physics
A new diffusion procedure for vortex methods
Journal of Computational Physics
Inviscid axisymmetrization of an elliptical vortex
Journal of Computational Physics
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
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
Modified interpolation kernels for treating diffusion and remeshing in vortex methods
Journal of Computational Physics
PPM: a highly efficient parallel particle-mesh library for the simulation of continuum systems
Journal of Computational Physics
Adaptive Node Refinement Collocation Method for Partial Differential Equations
ENC '06 Proceedings of the Seventh Mexican International Conference on Computer Science
Journal of Computational Physics
Multirate Runge-Kutta schemes for advection equations
Journal of Computational and Applied Mathematics
Discretization correction of general integral PSE Operators for particle methods
Journal of Computational Physics
A multiresolution remeshed Vortex-In-Cell algorithm using patches
Journal of Computational Physics
Hi-index | 31.45 |
We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.