Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations
SIAM Journal on Numerical Analysis
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Vortex methods with spatially varying cores
Journal of Computational Physics
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
Three-dimensional vortex methods for particle-laden flows with two-way coupling
Journal of Computational Physics
A general deterministic treatment of derivatives in particle methods
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods
Journal of Computational Physics
Variable order revised binary treecode
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
PPM: a highly efficient parallel particle-mesh library for the simulation of continuum systems
Journal of Computational Physics
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We present novel multiresolution particle methods with extended dynamic adaptivity in areas where increased resolution is required. In the framework of smooth particle methods we present two adaptive approaches: one based on globally adaptive mappings and one employing a wavelet-based multiresolution analysis to guide the allocation of computational elements. Preliminary results are presented from the application of these methods to problems involving the development of sharp vorticity gradients. The present particle methods are employed in large scale parallel computer architectures demonstrating a high degree of parallelization and enabling state of the art large scale simulations of continuum systems using particles.