scholarly journals Optimal Heat Distribution Using Asymptotic Analysis Techniques

2021 ◽  
Author(s):  
Zakaria Belhachmi ◽  
Amel Ben Abda ◽  
Belhassen Meftahi ◽  
Houcine Meftahi
Keyword(s):  
Asymptotic Expansion ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Numerical Experiments ◽  
Thermal Environment ◽  
Topological Derivative ◽  
Maximum Temperature ◽  
Heat Distribution ◽  
Two Dimensional ◽  
Optimal Heat

In this chapter, we consider the optimization problem of a heat distribution on a bounded domain Ω containing a heat source at an unknown location ω⊂Ω. More precisely, we are interested in the best location of ω allowing a suitable thermal environment. For this propose, we consider the minimization of the maximum temperature and its L2 mean oscillations. We extend the notion of topological derivative to the case of local coated perturbation and we perform the asymptotic expansion of the considered shape functionals. In order to reconstruct the location of ω, we propose a one-shot algorithm based on the topological derivative. Finally, we present some numerical experiments in two dimensional case, showing the efficiency of the proposed method.

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

scholarly journals INTERACTIONS BETWEEN MODERATELY CLOSE INCLUSIONS FOR THE LAPLACE EQUATION

2009 ◽  
Vol 19 (10) ◽  
pp. 1853-1882 ◽  
Author(s):  
VIRGINIE BONNAILLIE-NOËL ◽  
MARC DAMBRINE ◽  
SÉBASTIEN TORDEUX ◽  
GRÉGORY VIAL
Keyword(s):  
Asymptotic Expansion ◽  
Laplace Equation ◽  
Numerical Experiments ◽  
Characteristic Size ◽  
Superposition Method ◽  
Two Dimensional ◽  
First Order ◽  
Order Expansion ◽  
Single Inclusion ◽  
Reference Domain

The presence of small inclusions modifies the solution of the Laplace equation posed in a reference domain Ω0. This question has been studied extensively for a single inclusion or well-separated inclusions. In two-dimensional situations, we investigate the case where the distance between the holes tends to zero but remains large with respect to their characteristic size. We first consider two perfectly insulated inclusions. In this configuration we give a complete multiscale asymptotic expansion of the solution to the Laplace equation. We also address the situation of a single inclusion close to a singular perturbation of the boundary ∂Ω0. We also present numerical experiments implementing a multiscale superposition method based on our first order expansion.

Computational models of filtration gas combustion

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Yuri M. Laevsky ◽  
Tatyana A. Nosova
Keyword(s):  
Heat Flow ◽  
Numerical Experiments ◽  
Computational Models ◽  
Two Dimensional ◽  
Multidimensional Model ◽  
Gas Combustion ◽  
Total Enthalpy ◽  
Diffusive Flow ◽  
Temperature Heat ◽  
The One

AbstractA multidimensional model of filtration gas combustion is presented. The model is based on the system of conservation laws of ‘temperature – heat flow’, ‘mass–diffusive flow’ types with introducing the concept of total enthalpy flow. Results of numerical experiments are presented for the one- and two-dimensional problems for different conditions and parameters.

An adaptive wavelet collocation method for the optimal heat source problem

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahmood Khaksar-e Oshagh ◽  
Mostafa Abbaszadeh ◽  
Esmail Babolian ◽  
Hossein Pourbashash
Keyword(s):  
Heat Source ◽  
Numerical Technique ◽  
State Function ◽  
Adaptive Wavelet ◽  
Content Type ◽  
Optimal Heat ◽  
Wavelet Collocation Method ◽  
Collocation Approach ◽  
Interpolating Wavelets ◽  
Accurate Numerical Solution

Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

An obstacle problem for elliptic membrane shells

2018 ◽  
Vol 24 (5) ◽  
pp. 1503-1529 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare ◽  
Paolo Piersanti
Keyword(s):  
Vector Field ◽  
Asymptotic Analysis ◽  
Obstacle Problem ◽  
Displacement Vector ◽  
Middle Surface ◽  
Two Dimensional ◽  
Displacement Vector Field ◽  
Membrane Shells ◽  
Signorini Condition ◽  
Confinement Condition

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

scholarly journals Pedestrian Walking Behavior Revealed through a Random Walk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hui Xiong ◽  
Liya Yao ◽  
Huachun Tan ◽  
Wuhong Wang
Keyword(s):  
Numerical Experiments ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Pedestrian Flow ◽  
Alternating Direction Implicit Method ◽  
Walking Behavior ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Continuous Time Random Walks ◽  
High Order Compact Scheme

This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

A Two-Dimensional Conjugate Heat Transfer Model for Forced Air Cooling of an Electronic Device

1989 ◽  
Vol 111 (1) ◽  
pp. 41-45 ◽  
Author(s):  
A. Zebib ◽  
Y. K. Wo
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Electronic Device ◽  
Transfer Problem ◽  
Maximum Temperature ◽  
Transfer Model ◽  
Air Cooling ◽  
Two Dimensional ◽  
Component Design ◽  
Forced Air

Thermal analysis of forced air cooling of an electronic component is modeled as a two-dimensional conjugate heat transfer problem. The velocity field in a constricted channel is first computed. Then, for a typical electronic module, the energy equation is solved with allowance for discontinuities in the thermal conductivity. Variation of the maximum temperature with the average air velocity is presented. The importance of our approach in evaluating possible benefits due to changes in component design and the limitations of the two-dimensional model are discussed.

Sign in / Sign up

Export Citation Format

Share Document