2 citations · 2 across the 3 of their papers we have counts for
9 papers
Resolve the multitude of microscale interactions to model stochastic partial differential equations
A. J. Roberts
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dis…
A normal form of thin fluid film equations provides initial conditions
A. J. Roberts
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations…
Low-dimensional modelling of a generalized Burgers equation
Zhenquan Li, A. J. Roberts
Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is a…
A flexible error estimate for the application of centre manifold theory
Zhenquan Li, A. J. Roberts
In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend…
Modelling the dynamics of turbulent floods
Z. Mei, A. J. Roberts, Zhenquan Li
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to…
The accurate and comprehensive model of thin fluid flows with inertia on curved substrates
A. J. Roberts, Zhenquan Li
Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a compr…