A new formulation of the equivalent thermal in optimization of hydrothermal systems.
A one-dimensional spot welding model.
A semidiscretization scheme for a phase-field type model for solidification.
Adomian decomposition method for a nonlinear heat equation with temperature dependent thermal properties.
An application of the finite volume method to the bio-heat-transfer-equation in premature infants.
An approximate nonlinear projection scheme for a combustion model
The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE’s, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...
An approximate nonlinear projection scheme for a combustion model
The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE's, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...
Application of the multigrid methods for solving Stefan problem
Approximate solution of the nonlinear heat conduction equation in a semi-infinite domain.
Approximation of a solidification problem
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri,...
C++ tools to construct our user-level language
The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.
C++ Tools to construct our user-level language
The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++ to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.
Calculation of some integrals arising in heat transfer in geothermics.
Computation of bifurcated branches in a free boundary problem arising in combustion theory
Computation of bifurcated branches in a free boundary problem arising in combustion theory
We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter does not exceed a critical value . The latter is the limit of a decreasing sequence of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...
Conservation schemes for convection-diffusion equations with Robin boundary conditions
In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some...
Constructing a relativistic heat flow by transport time steps
Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions.
Dynamic optimal cooling control for continuous casting of steel
Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data
We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.