In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.
In the second part of the paper, we compare the solutions produced
in the framework of the conference “Mathematical and numerical
aspects of low Mach number flows” organized by INRIA and MAB in
Porquerolles, June 2004, to the reference solutions described in
Part 1. We make some recommendations on how to produce good
quality solutions, and list a number of pitfalls to be avoided.
There are very few reference solutions in the literature on
non-Boussinesq natural convection flows. We propose here a test
case problem which extends the well-known De Vahl Davis
differentially heated square cavity problem to the case of large
temperature differences for which the Boussinesq approximation is
no longer valid. The paper is split in two parts: in this first
part, we propose as yet unpublished reference solutions for cases
characterized by a non-dimensional temperature difference...
Over the past decade or so, there have been a large number of modelling approaches aimed
at elucidating the most important mechanisms affecting the formation of new capillaries
from parent blood vessels — a process known as angiogenesis. Most studies have focussed
upon the way in which capillary sprouts are initiated and migrate in response to
diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the
contexts of solid tumour...
For the Stokes problem in a two- or three-dimensional
bounded domain, we propose a new mixed finite element discretization which relies on
a nonconforming approximation of the velocity and a more accurate approximation of the
pressure. We prove that the velocity and pressure discrete spaces are compatible, in the
sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we
derive some error estimates.
As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments...