A Conservative Iterative-Based Zonal Decomposition Scheme for Conduction Heat Transfer Problems

1999 ◽  
Vol 121 (1) ◽  
pp. 169-173 ◽  
Author(s):  
O. E. Ruiz ◽  
W. Z. Black
Keyword(s):  
Finite Difference ◽  
Numerical Technique ◽  
Accurate Solution ◽  
Relaxation Parameter ◽  
Decomposition Technique ◽  
Rapid Convergence ◽  
Conduction Heat Transfer ◽  
Decomposition Scheme ◽  
Transient Problems ◽  
Transfer Problems

A new conservative iterative-based zonal decomposition technique for the solution of complex heat conduction problems is proposed. This numerical technique is based on dividing the domain into subdomains and ensuring that the heat flux and temperature are continuous at the boundary between subdomains. An example problem is used to illustrate the zonal decomposition technique for both steady and transient problems. This numerical technique results in accuracy which equals or exceeds traditional finite difference solutions and solution times which are significantly less than traditional finite difference solutions. A numerical relaxation parameter is introduced and its value is optimized to provide the most rapid convergence to an accurate solution.

New Mesh Relaxation Technique in Multi-Material ALE Applications

2004 ◽  
Author(s):  
K. Mahmadi ◽  
N. Aquelet ◽  
M. Souli
Keyword(s):  
High Pressures ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Relaxation Parameter ◽  
Numerical Results ◽  
Arbitrary Lagrangian Eulerian ◽  
Fine Mesh ◽  
Transient Problems ◽  
Control Mesh ◽  
Shock Fronts

The Arbitrary Lagrangian-Eulerian (ALE) method is a method that contains both pure Lagrangian and pure Eulerian formulations. It is assumed to be capable to control mesh geometry independently from material geometry. However for transient problems involving pressure wave, this method will not allow to maintain a fine mesh in the vicinity of the shock wave for accurate solution. A new mesh relaxation method for explicit multi-material arbitrary Lagrangian Eulerian finite element simulations has been developed to keep an as “Lagrange like” fluid mesh as possible as in the vicinity of shock fronts, while at the same time keeping the mesh distortions on an acceptable level. However, the relaxation parameter must be defined for general applications of high pressures, it is the objective of this work. In this paper we present numerical results of three shock waves problems. For every application, numerical results will be compared with the experimental results in order to improve to understanding how the relaxation parameter is chosen.

Multinode Unsteady Surface Element Method With Application to Contact Conductance Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 257-263 ◽  
Author(s):  
B. Litkouhi ◽  
J. V. Beck
Keyword(s):  
Numerical Technique ◽  
Three Dimensional ◽  
The Other ◽  
Surface Element ◽  
Variable Boundary ◽  
Transient Problems ◽  
Different Temperatures ◽  
Perfect Contact ◽  
Transfer Problems ◽  
Element Method

The unsteady surface element method is a powerful numerical technique for solution of linear transient two- and three-dimensional heat transfer problems. Its development originated with the need of solving certain transient problems for which similar or dissimilar bodies are attached one to the other over a part of their surface boundaries. In this paper a multinode unsteady surface element (MUSE) method for two arbitrary geometries contacting over part of their surface boundaries is developed and formulated. The method starts with Duhamel’s integral (for arbitrary time and space variable boundary conditions) which is then approximated numerically in a piecewise manner over time and the boundaries of interest. To demonstrate the capability of the method, it is applied to the problem of two semi-infinite bodies initially at two different temperatures suddenly brought into perfect contact over a small circular region. The results show excellent agreement between the MUSE solution and the other existing solutions.

Finite Difference Time Domain Simulations of Hybrid Neurotransducers Based Optical Microlasers

2020 ◽  
Author(s):  
Maurizio Manzo ◽  
Omar Cavazos
Keyword(s):  
Finite Difference ◽  
Chronic Traumatic Encephalopathy ◽  
Numerical Technique ◽  
Well Being ◽  
Infrared Light ◽  
Neuron Activity ◽  
Living Matter ◽  
Brain Functions ◽  
Laser Modes ◽  
The Brain

Abstract Different pathologies such as Alzheimer’s, Parkinson’s, Wilson’s diseases, and chronic traumatic encephalopathy due to blasts and impacts affect the brain functions altering the neuronal electrical activity. An important aspect of the brain study is the use of non-invasive, non-surgical methodologies that are suitable to the well-being of the patients. Only a portion of the electromagnetic field can be detected by applying sensors outside the scalp; in addition, surgery is often involved if sensors are applied in the subcutaneous region of the skull. Optical techniques applied to biomedical research and diagnostics have been spread during the last decades. For example, near infrared light (NIR) of spectral range goes from 800 nm to 1300 nm, it is harmless radiation for the living tissue, and can penetrate the living matter in depth as, it turns out that most of the living matter is transparent to the NIR light. Optical microlasers have been recently proposed as neurotransducers for minimally invasive neuron activity detection for the next generation of brain-computer interface (BCI) systems. They are lightweight, require low power consumption and exhibit low latency. This novel sensor that can be made of biocompatible material is coupled with a voltage sensitive dye; the fluorescence of the dye, which is excited by an external light source, is used to generate optical (laser) modes. Any variation in the neurons’ membrane electric potential via evanescent field’s perturbation turn affect the shifting of these laser modes. In order to reduce the energy required to power these devices and to improve their optical emission, metal nanoparticles can be coupled in order to use their plasmonic effect. In this paper, finite-difference timedomain (FDTD) numerical technique is used to analyze the performances on a dye-doped microlaser. Purcell effect and resonant wavelengths are observed.

A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

2021 ◽  
Author(s):  
Tesfaye Aga Bullo ◽  
Guy Aymard Degla ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Variable Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Uniform Mesh

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

scholarly journals A NOTE ON THE CONSTANT THERMAL CONDUCTIVITY HYPOTHESIS AND ITS CONSEQUENCE FOR CONDUCTION HEAT TRANSFER PROBLEMS

2014 ◽  
Vol 13 (2) ◽  
pp. 48
Author(s):  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
High Temperature ◽  
Heat Generation ◽  
Strong Dependence ◽  
Temperature Gradients ◽  
Conduction Heat Transfer ◽  
Kirchhoff Transformation ◽  
Constant Thermal Conductivity ◽  
Transfer Problems

This work discuss the usual constant conductivity assumption and its consequences when a given material presents a strong dependence between the temperature and the thermal conductivity. The discussion is carried out considering a sphere of silicon with a given heat generation concentrated in a vicinity of its centre, giving rise to high temperature gradients. This particular case is enough to show that the constant thermal conductivity hypothesis may give rise to very large errors and must be avoided. In order to surpass the mathematical complexity, the Kirchhoff transformation is used for constructing the solution of the problem. In addition, an equation correlating thermal conductivity and the temperature is proposed.

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