Two-dimensional diffusion equations coupled with electron, ion and photon temperatures are widely used to approximately describe the radiation evolution of energy across multiple materials and perceive the exchange of energy among electrons, ions and photons for numerical researches on laser-driven implosion of a fuel capsule in inertial confinement fusion experiments. The numerical solution of such equations is always fascinating because of its strong nonlinear phenomena and strong discontinuous interfaces. On the basis of UG framework, this article successfully solves such equations on two-dimensional unstructured grid applied with full implicit finite volume discrete scheme and parallel adaptive multigrid algorithm. Significant numerical results are given and analyzed.