New Boundary Conditions For Objects
In A Continuum Ionized Medium With
An External Electric Field
Author(s)
R. Godard
Abstract
Mathematical models for conducting or non-conducting spherical objects
immersed in a continuum-ionized medium are well known and have wide
applications. In the solution of a system of three coupled non-linear equations
the classical fluid model consists of: (1) the continuity equation, (2) the transport
equations, and (3) the Poisson equation. One important and reasonable
approximation consists of replacing the Poisson equation by a Laplace equation.
The numerical algorithm becomes very complex if we superpose an external
electric field or convection effects. Even if numerical analysts have used upwind
methods it is clear that if the wind or the external electric field becomes
dominant, the structure of the partial differential equations is modified, and the
problem will not be elliptic. In particular, the transition regime between
diffusion effects and convection effects is extremely difficult to simulate and
numerically unstable. In the classical fluid model, the classical boundary
conditions are fixed for the potential and also for the density of species,
i.e. ( , ) 0 N a θ ± = where a is, for example, the radius of a dust particle. However,
these fixed boundary conditions do not satisfy the convection problem. Using
the linearity properties of a Laplace operator, we have introduced new surface
boundary conditions. We superpose both boundary conditions for a diffusion
problem and a convection problem. Boundary conditions are floating, according
to the strength of the external electric field or the convection effects. The
numerical scheme becomes stable. Simulations have been carried out for an axisymmetrical
problem, using an adaptable computational grid.
Keywords: diffusion-convection problems, electric field charging process,
floating boundary conditions, upwind schemes, finite element methods.
Keywords
diffusion-convection problems, electric field charging process,
floating boundary conditions, upwind schemes, finite element methods
Related Book
Other papers in this volume
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