A local character based method for solving linear systems of radiation diffusion problems
A local character based method for solving linear systems of radiation diffusion problems
复制标题
基于局部特征的线性系统辐射扩散问题求解方法
DOI：
10.1016/j.jcp.2019.109218
复制
发表时间：
2019
影响因子：
4.1
通讯作者：
徐新海
中科院分区：
文献类型：
--
作者：
叶帅;安恒斌;徐新海
辐射扩散问题是一类时变非线性方程。求解辐射扩散方程时，在每个时间步长的非线性迭代中得到许多线性系统。线性方程的代价在辐射扩散应用的数值模拟中占主导地位，如惯性约束聚变等。在实际应用中，通常采用迭代法求解线性系统。此外，通常将前一次非线性迭代的解或前一次时间步长的解作为求解当前线性方程的初始猜测。由于ICF具有较强的局部特性，随着非线性迭代和时间步长的推进，线性系统的解在某些局部区域变化剧烈，而在其他区域变化不大甚至没有变化。本文提出了一种基于局部特征的线性系统辐射扩散问题求解方法。该方法分为三个步骤：首先，构造局部域（代数域）；其次，对局部子系统进行了求解；最后，对整个系统进行求解。给出了两种构造局部域的方法。一种是基于空间梯度，另一种是基于残差。对一个二维热传导模型问题和两个实际应用模型，即多群辐射扩散方程和三种温度能量方程进行了数值测试。测试结果表明，采用基于局部特征的方法可以显著缩短求解线性系统的时间。
The radiation diffusion problem is a kind of time-dependent nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations dominates the numerical simulation of radiation diffusion applications, such as inertial confinement fusion, etc. Usually, iterative methods are used to solve the linear systems in a real application. Moreover, the solution of the previous nonlinear iteration or the solution of the previous time step is typically used as the initial guess for solving the current linear equations. Because of the strong local character in ICF, with the advancing of nonlinear iteration and time step, the solution of the linear system changes dramatically in some local domain, and changes mildly or even has no change in the rest domain.In this paper, a local character-based method is proposed to solve the linear systems of radiation diffusion problems. The proposed method consists of three steps: firstly, a local domain (algebraic domain) is constructed; secondly, the subsystem on the local domain is solved; and lastly, the whole system will be solved. Two methods are given to construct the local domain. One is based on the spatial gradient, and the other is based on the residual. Numerical tests for a two-dimensional heat conduction model problem, and two real application models, the multi-group radiation diffusion equations and the three temperature energy equations, are conducted. The test results show that the solution time for solving the linear system can be reduced dramatically by using the local character-based method.