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We consider in this paper a mathematical and numerical model to design an industrial software solution able to handle real complex furnaces configurations in terms of geometries, atmospheres, parts positioning, heat generators and physical thermal phenomena. A three dimensional algorithm based on stabilized finite element methods (SFEM) for solving the momentum, energy, turbulence and radiation equations is presented. An immersed volume method (IVM) for thermal coupling of fluids and solids is introduced...
In this paper, a phase field system of Penrose–Fife type with
non–conserved order parameter is considered.
A class of time–discrete schemes for an initial–boundary
value problem for this phase–field system is presented.
In three space dimensions, convergence is proved and
an error estimate
linear with respect to the time–step size
is derived.
We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms of the associated chemical potential fields are bounded uniformly, where and is the dimension of the domain. We show that the limit interface as tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.
We consider a domain decomposition method for some unsteady
heat conduction problem in composite structures.
This linear model problem is obtained by homogenization of thin layers
of fibres embedded into some standard material.
For ease of presentation we consider the case of two space dimensions only.
The set of finite element equations obtained by the backward Euler scheme
is parallelized in a problem-oriented fashion by some noniterative overlapping
domain splitting method,
eventually enhanced...
The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional...
The present paper is devoted to the computation of single phase or
two phase flows using the single-fluid approach. Governing equations
rely on Euler equations which may be supplemented by conservation
laws for mass species. Emphasis is given on numerical modelling
with help of Godunov scheme or an approximate form of Godunov scheme
called VFRoe-ncv based on velocity and pressure variables. Three
distinct classes of closure laws to express the internal energy in
terms of pressure, density...
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