“Consistent boundary conditions for computational fluid dynamics modelling in steady, incompressible, two-dimensional flow”
by Prof. David Wood, 11/29

A good choice of far-field boundary conditions (BCs) for the simulation
of airfoil and other aerodynamic flows, allows the minimization of the
domain size for a given level of error or the converse. Simulations of a
NACA 0012 airfoil for a range of angles up to 45 degrees using OpenFOAM,
show the need for consistency with the Kutta-Joukowsky (KJ) equation for
the lift in the form of a point vortex boundary condition. This is not
surprising, given that the KJ equation is well-known. What is less
well-known is that consistency with the drag requires a point source
BC. A combined point source, point vortex BC is easy to implement, but
still may be inconsistent with the moment equation for the body. This
may adversely affect the accuracy of the torque computed for, say,
vertical axis turbines which are often simulated in
two-dimensions. Methods of achieving consistency with the moment
equation will be discussed and a surprisingly simple correction for the
use of commonly-used, but inconsistent BCs, will be described.

“Beyond the Richards equation: two-phase flow in an unsaturated
porous medium”
By Prof. Michael Vynnycky, 12/9

Flow in an unsaturated porous medium is typically modelled using the
Richards equation, which is unquestioningly believed to be an accurate
enough approximation when the viscosity of the fluid being displaced,
e.g. air, is much smaller than that of the infiltrating fluid, e.g. oil
or water. Here, we apply asymptotic and numerical methods to a
one-dimensional problem when this is not the case. With the viscosity
ratio as a small parameter, we find that the Richards equation gives a
leading-order solution that is not uniformly valid over the whole domain
of interest. Instead, whilst the Richards equation holds for the bulk
flow, the problem has a derivative (or one-sided corner) layer for the
saturation function at the infiltration boundary, i.e. there is a
boundary layer in the spatial derivative of the saturation, but not in
saturation itself. Although seemingly insignificant, this has a dramatic
effect on the time taken to fill the porous medium: instead of filling
exponentially quickly, it fills algebraically slowly. As a consequence,
using the Richards equation will dramatically underestimate the time
taken to fill a porous medium. Numerical computations are provided to
underscore these asymptotic predictions.