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An efficient iterative method for radiation heat conduction problems
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-03-13 , DOI: 10.1002/fld.4977 Yanzhong Yao 1 , Shuai Miao 1, 2 , Guixia Lv 1
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-03-13 , DOI: 10.1002/fld.4977 Yanzhong Yao 1 , Shuai Miao 1, 2 , Guixia Lv 1
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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.
中文翻译：
一种求解辐射热传导问题的高效迭代方法
为了有效地解决辐射流体动力学问题，设计良好的迭代方法至关重要。在实际应用中，传统的Picard迭代法由于具有实现简单、无需雅可比矩阵计算等优点而得到广泛应用。但是，它的收敛速度非常低。针对“收敛慢”问题，本文通过松弛技术提出了一种基于简单迭代方法的加速策略，并构建了一个通用的迭代加速框架，在形式上将简单迭代方法与一些二阶迭代方法相结合。通过这种加速策略，我们基于有限体积方案的特点，开发并分析了一种改进的非线性热方程迭代方法，并与传统的皮卡德方法进行了比较。数值结果表明，改进的迭代方法在保持其主要优点的同时比传统的Picard方法快得多，并且计算网格越细，收敛速度越接近二阶。此外，根据加速度框架的指导，很容易设计出新颖的辐射热传导方程迭代方案。
更新日期：2021-03-13
中文翻译：
一种求解辐射热传导问题的高效迭代方法
为了有效地解决辐射流体动力学问题，设计良好的迭代方法至关重要。在实际应用中，传统的Picard迭代法由于具有实现简单、无需雅可比矩阵计算等优点而得到广泛应用。但是，它的收敛速度非常低。针对“收敛慢”问题，本文通过松弛技术提出了一种基于简单迭代方法的加速策略，并构建了一个通用的迭代加速框架，在形式上将简单迭代方法与一些二阶迭代方法相结合。通过这种加速策略，我们基于有限体积方案的特点，开发并分析了一种改进的非线性热方程迭代方法，并与传统的皮卡德方法进行了比较。数值结果表明，改进的迭代方法在保持其主要优点的同时比传统的Picard方法快得多，并且计算网格越细，收敛速度越接近二阶。此外，根据加速度框架的指导，很容易设计出新颖的辐射热传导方程迭代方案。
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