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An efficient iterative method for radiation heat conduction problems
Author(s) -
Yao Yanzhong,
Miao Shuai,
Lv Guixia
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4977
Subject(s) - iterative method , jacobian matrix and determinant , acceleration , rate of convergence , relaxation (psychology) , convergence (economics) , mathematical optimization , successive over relaxation , mathematics , local convergence , computer science , key (lock) , psychology , social psychology , physics , computer security , classical mechanics , economics , economic growth
To solve radiation hydrodynamics problems efficiently, a well‐designed iterative method is crucial. In practical applications, the conventional Picard iterative method is widely used due to its advantages, such as implementation simplicity and no Jacobian matrix computations. However, its convergence rate is very low. To address the “slow convergence” problem, we present an acceleration strategy based on simple iterative methods by the relaxation technique in this article, and construct a general iteration acceleration framework which unifies simple iterative methods with some second order iterative methods in form. By this acceleration strategy, we develop and analyze an improved iterative method for the nonlinear heat equation based on the characteristics of the finite volume schemes, and compare with the conventional Picard method. Numerical results indicate that, the improved iterative method is much faster than the conventional Picard method while retaining its main advantages, and the finer the computational grids become, the closer the convergence rate approaches to the second order. In addition, according to the guidance of the acceleration framework, it is easy to design novel iterative schemes for radiation heat conduction equations.