Numerical model of an electropaint process with applications to the automotive industry

A steady-state model is developed for the process known as electropainting.The model consists of Laplace's equation with boundary conditionsin the form of inequalities and complementarity relations. Numericalmethods based on the boundary-element method are applied tosolve the equations on realistic industrial geometries, whenwe consider a test piece used in the assessment of the capabilityof particular paints, and in three dimensions when we considerthe problem of coating car roofs. Comparisons are made betweenthe numerical solutions and available experimental data.     

Percolation in Gently Sloping Beaches

We analyse flow through a porous medium when the free boundarybetween the saturated and dry parts of the medium is everywherevery close to the upper surface of the medium, i.e. the beach,which is assumed to be nearly horizontal. For small beach slopes,a heuristic asymptotic formulation is derived and analysed usingthe theory of variational inequalities. This justifies the useof a finite-element approximation whose results are comparedwith explicit solutions in special cases.     

The Numerical Solution of a Minimization Problem Associated with a Free Surface Flow

The solution of the differential equation governing the seepageof fluid through a porous dam can be shown to be equivalentto the minimization of a quadratic functional over a fixed rectangularregion. The latter problem is solved using the method of finiteelements, and the results compared with earlier computations.An analysis of the singularity at the separation point is usedto find the position of the separation point.     

A Model for an Electropaint Process

A simple time-dependent model is proposed for the process ofpainting a metal surface by electrodeposition. The problem isthen to solve the Laplace equation in a given region with afree boundary on a part of its surface. A related steady problemis considered. Numerical solutions to examples of both problemsare presented. We also discuss the existence and regularityof the solutions to the steady problem and find the exact solutionto a one-dimensional unsteady problem. In certain cases we areable to derive approximate solutions for other unsteady problems.     

Numerical Modelling of PIN Diodes

The coupled non-linear partial differential equations describingthe behaviour of PIN diodes are solved using a conservativefinite-difference scheme. For such problems the conservationof certain quantities is particularly important and the consistencyof the numerical scheme is demonstrated. Problems are consideredin cylindrical polar co-ordinates, and particular attentionis paid to the correct discretization of the boundary conditions.The modelling of large thin diodes is also considered. Numericalresults illustrating various features are presented.