Abstract We present an implicit numerical method to solve the time-dependent equations of radiation hydrodynamics (RHD) in axial symmetry assuming hydrostatic equilibrium perpendicular to the equatorial plane (1+1D) of a gaseous disk. The equations are formulated in conservative form on an adaptive grid and the corresponding fluxes are calculated by a spacial second order advection scheme. Self-gravity of the disk is included by solving the Poisson equation. We test the resulting numerical method through comparison with a simplified analytical solution as well as through the long term viscous evolution of protoplanetary disk when due to viscosity matter is transported towards the central host star and the disk depletes. The importance of the inner boundary conditions on the structural behavior of disks is demonstrated with several examples.

中文翻译：

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1+1D 隐式磁盘计算

摘要 我们提出了一种隐式数值方法来求解轴对称辐射流体动力学 (RHD) 的瞬态方程，假设流体静力平衡垂直于气态盘的赤道面 (1+1D)。方程在自适应网格上以保守形式制定，相应的通量通过空间二阶平流方案计算。圆盘的自重力通过求解泊松方程包括在内。我们通过与简化的解析解进行比较以及通过原行星盘的长期粘性演化来测试所得数值方法，当由于粘性物质向中央主星输送并且盘耗尽时。几个例子证明了内部边界条件对圆盘结构行为的重要性。