Fully implicit 1D radiation hydrodynamics: Validation and verification
Fully implicit 1D radiation hydrodynamics: Validation and verification
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DOI：
10.1016/j.jcp.2010.06.031
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
K. Ghosh;S. Menon
中科院分区：
文献类型：
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作者：
K. Ghosh;S. Menon
本文发展了一种全隐式有限差分格式来求解与辐射输运耦合的流体动力学方程。用离散坐标法求解了含时辐射输运方程，并充分考虑了辐射相互作用产生的能量流。在每个时间步求解一个三对角矩阵系统，以隐式地确定水动力变量。在平面几何条件下，用全隐式辐射流体动力学程序得到的结果与辐射驱动强激波在铝中传播的标度律符合得很好。对于点爆炸问题，将自相似解与球面几何中纯流体动力学情形的结果进行了比较。当辐射相互作用也被考虑时，所得结果与较低输入能量的点爆炸热传导的结果一致。因此，基准的代码，自收敛的方法w.r.t.对平面问题和球面问题的时间步长进行了详细的研究。空间以及时间收敛率是100%，从质量，动量和能量守恒方程的不同形式的预期。这表明，该码的渐近收敛速度是适当实现的。
A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tridiagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry. Results obtained when radiation interaction is also accounted agree with those of point explosion with heat conduction for lower input energies. Having, thus, benchmarked the code, self convergence of the method w.r.t. time step is studied in detail for both the planar and spherical problems. Spatial as well as temporal convergence rates are ≃1 as expected from the difference forms of mass, momentum and energy conservation equations. This shows that the asymptotic convergence rate of the code is realized properly.