Simulations of radiation hydrodynamics and radiative magnetohydrodynamics by collocation spectral methods

During recent years, considerable attention is given to the study of mixed convection and thermal radiation, and the study of radiative magnetohydrodynamics (R-MHD). There are lots of practical applications, such as, nuclear power plants, gas turbines, various propulsion devices for aircraft, missiles, satellites and space vehicles, thermal energy storage, and polymer industry. In the communication of numerical simulation, the solution of coupled heat transfer, fluid flow, thermal radiation and magnetohydrodynamics (MHD) includes solving the Navier-Stokes equations with buoyancy or magnetic force terms, the energy equation with radiative source term, the radiative transfer equation (RTE), and the electrical potential equation. These governing equations are usually partial differential equations except for the RTE which is a integral-differential (first order) equation. It is difficult to use only one numerical method to solve all these equations. Here, we develop the collocation spectral methods (CSM) to solve all above governing equations. If the cases are transient, the projection scheme is adopted for the temporal discretization. For the numerical procedure, the direct solution part can be as much as possible in our projection collocation spectral methods. Due to the numerical simulations of the radiation hydrodynamics (R-HD) and R-MHD with high efficiency and accuracy, lots of complex phenomena can be analyzed successfully and many significant conclusions are obtained.