Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.

Electric field strengths and ion trajectories in sharp-edge field ionization sources

On the presumption that a sharp edge may be represented by a hyperbola, a conformal transformation method is used to derive electric field equations for a sharp edge suspended above a flat plate. A further transformation is then introduced to give electric field components for a sharp edge suspended above a thin slit. Expressions are deduced for the field strength at the vertex of the edge in both arrangements. The calculated electric field components are used to compute ion trajectories in the simple edge/flat-plate case. The results are considered in relation to future study of ion focusing and unimolecular decomposition of ions in field ionization mass spectrometers.

An hr-adaptive discontinuous Galerkin method for advection-diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.