scholarly journals A consistent approach to solving the radiation diffusion equation

2003 ◽  
Vol 10 (5) ◽  
pp. 1829-1845 ◽  
Author(s):  
James H. Hammer ◽  
Mordecai D. Rosen
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Consistent Approach

Self-similar solutions for a nonlinear radiation diffusion equation

2006 ◽  
Vol 13 (9) ◽  
pp. 092703 ◽  
Author(s):  
Josselin Garnier ◽  
Guy Malinié ◽  
Yves Saillard ◽  
Catherine Cherfils-Clérouin
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Nonlinear Radiation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals The heat radiation diffusion equation: Explicit analytical solutions by improved integral-balance method

2018 ◽  
Vol 22 (2) ◽  
pp. 777-788 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Diffusion Equation ◽  
Analytical Solutions ◽  
Approximate Solutions ◽  
Step Change ◽  
Balance Method ◽  
Heat Radiation ◽  
Integration Technique ◽  
Residual Function ◽  
Radiation Diffusion ◽  
Closed Form Solutions

Approximate explicit analytical solutions of the heat radiation diffusion equation by applying the double integration technique of the integral-balance method have been developed. The method allows approximate closed form solutions to be developed. A problem with a step change of the surface temperature and two problems with time dependent boundary conditions have been solved. The error minimization of the approximate solutions has been developed straightforwardly by minimization of the residual function of the governing equation.

Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

2013 ◽  
Vol 14 (5) ◽  
pp. 1287-1303 ◽  
Author(s):  
Rongpei Zhang ◽  
Xijun Yu ◽  
Jiang Zhu ◽  
Abimael F. D. Loula ◽  
Xia Cui
Keyword(s):  
Diffusion Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Implicit Integration ◽  
Interior Penalty ◽  
Radiation Diffusion ◽  
Factor Method ◽  
Equilibrium Radiation ◽  
Non Equilibrium

AbstractWeighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semi-implicit integration factor method to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.

An efficient solving method for nonlinear convection diffusion equation

2018 ◽  
Vol 28 (1) ◽  
pp. 173-187 ◽  
Author(s):  
Xia Cui ◽  
GuangWei Yuan ◽  
ZhiJun Shen
Keyword(s):  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Induction Hypothesis ◽  
Function Analysis ◽  
Second Order ◽  
Nonlinear Convection ◽  
Radiation Diffusion ◽  
Content Type ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

Purpose This paper aims to provide a well-behaved nonlinear scheme and accelerating iteration for the nonlinear convection diffusion equation with fundamental properties illustrated. Design/methodology/approach A nonlinear finite difference scheme is studied with fully implicit (FI) discretization used to acquire accurate simulation. A Picard–Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis reasoning technique, the L∞ (H1) convergence of the scheme is proved despite the difficulty because of the combination of conservative diffusion and convection operator. Other properties are established consequently. Furthermore, the algorithm is extended from first-order temporal accuracy to second-order temporal accuracy. Findings Theoretical analysis shows that each of the two FI schemes is stable, its solution exists uniquely and has second-order spatial and first/second-order temporal accuracy. The corresponding PN iteration has the same order of accuracy and quadratic convergent speed. Numerical tests verify the conclusions and demonstrate the high accuracy and efficiency of the algorithms. Remarkable acceleration is gained. Practical implications The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems. Originality/value The FI schemes and iterations for the convection diffusion problem are proposed with their properties rigorously analyzed. The induction hypothesis reasoning method here differs with those for linearization schemes and is applicable to other nonlinear problems.

A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation

2014 ◽  
Vol 258 ◽  
pp. 338-358 ◽  
Author(s):  
Thomas M. Evans ◽  
Scott W. Mosher ◽  
Stuart R. Slattery ◽  
Steven P. Hamilton
Keyword(s):  
Monte Carlo ◽  
Diffusion Equation ◽  
Thermal Radiation ◽  
Radiation Diffusion ◽  
Acceleration Method
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