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...
Computational approaches to some inverse problems from engineering practice
Development of engineering structures and technologies frequently works with advanced materials, whose properties, because of their complicated microstructure, cannot be predicted from experience, unlike traditional materials. The quality of computational modelling of relevant physical processes, based mostly on the principles of classical thermomechanics, is conditioned by the reliability of constitutive relations, coming from simplified experiments. The paper demonstrates some possibilities of...
Computational approaches to the design of low-energy buildings
European and Czech directives and technical standards, approved in several last years, force substantial changes in thermal behaviour of all buildings, including new and reconstructed one- or more-family houses, block of fl ats, etc., especially radical decrease of their energy requirements. This stimulates the development of advanced materials, structures and technologies. Since no reliable experience with their design is available, robust and non-expensive computational simulation approaches,...
Computational design optimization of low-energy buildings
European directives and related national technical standards force the substantial reduction of energy consumption of all types of buildings. This can be done thanks to the massive insulation and the improvement of quality of building enclosures, using the simple evaluation assuming the one-dimensional stationary heat conduction. However, recent applications of advanced materials, structures and technologies force the proper physical, mathematical and computational analysis coming from the thermodynamic...
Computational modelling of thermal consumption of buildings with controlled interior temperature
New materials, structures and technologies used in civil engineering impeach traditional evaluations of the annual thermal consumption of buildings, based on the quasi-stationary estimate of the thermal resistance of the building envelope, or some operational parts of such building with the guaranteed temperature. The complete proper physical analysis, applying the principles of thermodynamics and appropriate constitutive relations for particular material layers and air in rooms, is not realistic...
Computational studies of anisotropic diffuse interface model of microstructure formation in solidification
Conjugate heat transfer of mixed convection for viscoelastic fluid past a stretching sheet.
Conjugate problems in convective heat transfer: review.
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...
Constitutive theory in general relativity: spin--material in spaces with torsion.
Constructing a relativistic heat flow by transport time steps
Constructive analysis and thermodynamics formulations.
Control of Stefan Problems by Means of Linear-Quadratic Defect Minimization.
Convection-radiation heat transfer in a nonlinear fluid with temperature-dependent viscosity.
Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions.
Convergence to equilibria for a three-dimensional conserved phase-field system with memory.
Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys.
Convexity and uniqueness in a free boundary problem arising in combustion theory.
We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such thatut = Δu, in Ω,u = 0 and |∇u| = 1, on Γ := ∂Ω ∩ QT,u(·,0) = u0, on Ω0,where Ω0 is a given domain in Rn and u0 is a positive and continuous function in Ω0, vanishing on ∂Ω0. If Ω0 is convex and u0 is concave in Ω0, then we show that (u,Ω) is unique and the time sections...
Cooling of a layered plate under mixed conditions.