69 citations · 177 across the 9 of their papers we have counts for
9 papers
Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters
R. A. Brownlee, J. Levesley, D. Packwood +1
We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include fl…
Stable simulation of fluid flow with high-Reynolds number using Ehrenfests' steps
R. A. Brownlee, A. N. Gorban, J. Levesley
The Navier--Stokes equations arise naturally as a result of Ehrenfests' coarse-graining in phase space after a period of free-flight dynamics. This point of view allows for a very…
Extending the range of error estimates for radial approximation in Euclidean space and on spheres
R. A. Brownlee, E. H. Georgoulis, J. Levesley
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to gi…
Error estimates for interpolation of rough data using the scattered shifts of a radial basis function
R. A. Brownlee
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artif…
Approximation orders for interpolation by surface splines to rough functions
R. A. Brownlee, W. A. Light
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between a…
Nonequilibrium entropy limiters in lattice Boltzmann methods
R. A. Brownlee, A. N. Gorban, J. Levesley
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not…