论文标题
迈向用于辐射转移的M1模型的Multigrid方法
Towards a multigrid method for the M1 model for radiative transfer
论文作者
论文摘要
我们为无源项的M1辐射传输模型提供了几何多机求解器。在辐射流体动力学应用中，由于相对于流体速度的快速传播速度，因此需要隐式转移辐射转移。 M1模型是双曲线，可以通过HLL求解器离散，其时间隐含的集成可以使用非线性Jacobi方法完成。可以表明，这种迭代方法始终保留可允许的状态，例如阳性辐射能和降低的通量小于1。要减少求解器收敛所需的迭代次数，从而降低计算成本，我们提出了一种几何多元算法。不幸的是，这种方法无法保存可允许的状态。为了保留可允许的状态，我们引入了伪时间，以便在粗网格上解决问题的解决方案是伪时间中微分方程的稳态状态。我们提出了初步结果，显示了该方法中使用的多移民水平数量的迭代数量和计算成本的减少。这些结果表明，非线性多机方法可以用作诸如M1模型的双曲线系统的鲁棒隐式求解器。
We present a geometric multigrid solver for the M1 model of radiative transfer without source terms. In radiative hydrodynamics applications, the radiative transfer needs to be solved implicitly because of the fast propagation speed of photons relative to the fluid velocity. The M1 model is hyperbolic and can be discretized with an HLL solver, whose time implicit integration can be done using a nonlinear Jacobi method. One can show that this iterative method always preserves the admissible states, such as positive radiative energy and reduced flux less than 1. To decrease the number of iterations required for the solver to converge, and therefore to decrease the computational cost, we propose a geometric multigrid algorithm. Unfortunately, this method is not able to preserve the admissible states. In order to preserve the admissible state states, we introduce a pseudo-time such that the solution of the problem on the coarse grid is the steady state of a differential equation in pseudo-time. We present preliminary results showing the decrease of the number of iterations and computational cost as a function of the number of multigrid levels used in the method. These results suggest that nonlinear multigrid methods can be used as a robust implicit solver for hyperbolic systems such as the M1 model.
