The Study And Application Of Nine Point Scheme For Radiation Heat Conduction Problems

The accurate and fast method for numerically solving radiation heat conduction, associated with the applications of astrophysics physics and Inertial Confinement Fusion (ICF) etc., plays an important role in the numerical simulation of radiation hydrodynamics. In the 1960's, the computer performance was limited and the computational costs were too high if the non-splitting methods were used. So the splitting methods, such as the Alternating Direction Methods (ADM) and Fractional Steps Methods (FSM) were developed to solve the multi-dimensional radiation heat equations by a simple reduction of the multidimensional problem to a sequence of one-dimensional problems. It follows that the splitting methods become very popular in the numerical simulation of many application problems.With the rapid development of modern computers and the numerical schemes, the non-splitting methods have been used in multi-dimensional application programs. In this paper, based on the Nine Point Schemes (NPS) for radiation heat conduction, the difference between the splitting methods (ADM) and the non-splitting methods is investigated. On distorted meshes, the accu-racy and efficiency of NPS applied with different cell-vertex interpolation methods and iterative methods have been compared. The main results in this thesis are the following:(1) The Continuous Flux Bilinear Interpolation (CFBI) method of cell-vertex temperature is designed for NPS and compared with others interpolation methods. Numerical experiments demonstrate that the accuracy of NPS is improved by using CFBI method.(2) The different nonlinear iterative methods have been analyzed for radiation heat conduction equations. Numerical experiments show that the Jacobian free Newton-Krylov (JFNK) method is better in accuracy than Fully Implicit Picard (FIP) for NPS, if it is matched with properly interpolation methods of cell-vertex temperature. Moreover, the average number of nonlinear iterations per time step and the total linear iterations of JFNK method have been decreased significantly, though the total runtime of JFNK is more than that of FIP.(3) The characteristic and difference between the splitting method and the non-splitting method is investigated for NPS. The numerical results demonstrates that the accuracy of non-splitting method with large time-step is better than that of splitting method on distorted meshes. The non-splitting method can overcome the negative effects of distorted meshes, although it spends much more CPU time than splitting method.(4) Two dimensional radiation hydrodynamics code RH2D is updated by the non-splitting method based on NPS for radiation heat conduction equations. Numerical results for a practical problem simulated by code RH2D with the splitting method and the non-splitting method are compared. It is indicated that the non-splitting method of NPS does improve numerical accuracy, and shows smaller energy conservation errors.