The radiation hydrodynamics equations for smoothed particle hydrodynamics are derived by operator splitting the radiation and hydrodynamics terms, including necessary terms for material motion, and discretizing each of the sets of equations separately in time and space. The implicit radiative transfer discussed in the first paper of this series is coupled to explicit smoothed particle hydrodynamics. The result is a multi-material meshless radiation hydrodynamics code with arbitrary opacities and equations of state that performs well for problems with significant material motion. The code converges with second-order accuracy in space and first-order accuracy in time to the semianalytic solution for the Lowrie radiative shock problem and has competitive performance compared to a mesh-based radiation hydrodynamics code for a multi-material problem in two dimensions and an ablation problem inspired by inertial confinement fusion in two and three dimensions.

通过将辐射和流体动力学项（包括物质运动的必要项）分开，并在时间和空间上分别离散每个方程组，可以得出用于平滑粒子流体动力学的辐射流体力学方程。本系列第一篇文章中讨论的隐式辐射传递与显式平滑粒子流体动力学耦合。结果是具有任意不透明性和状态方程的多材料无网格辐射流体力学代码，可很好地解决重大材料运动问题。