A fast algorithm for particle simulations
Journal of Computational Physics
Resurrecting Core Spreading Vortex Methods: A New Scheme That Is Both Deterministic and Convergent
SIAM Journal on Scientific Computing
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
Lagrangian methods for the tensor-diffusivity subgrid model
Journal of Computational Physics
A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow
Journal of Computational Physics
A vortex particle method for two-dimensional compressible flow
Journal of Computational Physics
Achieving High-Order Convergence Rates with Deforming Basis Functions
SIAM Journal on Scientific Computing
A Comparative Study of Lagrangian Methods Using Axisymmetric and Deforming Blobs
SIAM Journal on Scientific Computing
Evaluation of the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements
SIAM Journal on Scientific Computing
Journal of Computational Physics
A fast resurrected core-spreading vortex method with no-slip boundary conditions
Journal of Computational Physics
SIAM Journal on Scientific Computing
Global field interpolation for particle methods
Journal of Computational Physics
GPU accelerated simulations of bluff body flows using vortex particle methods
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot-Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb-Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1^/^3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.