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Computational design optimization of low-energy buildings

Vala, Jiří (2017)

Proceedings of Equadiff 14

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

Vala, Jiří (2017)

Programs and Algorithms of Numerical Mathematics

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...

Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron, Jacques Rappaz (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Convexity and uniqueness in a free boundary problem arising in combustion theory.

Arshak Petrosyan (2001)

Revista Matemática Iberoamericana

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...

Coupled heat transport and Darcian water flow in freezing soils

Krupička, Lukáš, Štefan, Radek, Beneš, Michal (2013)

Programs and Algorithms of Numerical Mathematics

The model of coupled heat transport and Darcian water flow in unsaturated soils and in conditions of freezing and thawing is analyzed. In this contribution, we present results concerning the existence of the numerical solution. Numerical scheme is based on semi-implicit discretization in time. This work illustrates its performance for a problem of freezing processes in vertical soil columns.

Coupling of chemical reaction with flow and molecular transport

Ulrich Maas (1995)

Applications of Mathematics

During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries,...

Currently displaying 101 – 120 of 528