A Study To Numerical Simulation Of Multicomponent Compressible Large Distortion Flows And Radiation Heat Conduction Problems

This dissertation is devoted to the study of two subjects which are important for the numerical simulation of implosion compression process of inertial confinement fusion(ICF).The first subject is to search for high accuracy order Eulerian methods for the numerical simulation of multicomponent compressible large distortion flow problems and fluid interface instability problems in implosion compression process,the other one is to find more efficient numerical methods for solving three-temperature radiation heat conduction equations related to the implosion compression process.We are among the first to investigate systematically the feasibility of high order weighted essentially non-oscillatory(WENO) schemes when applied to the numerical simulation of ICF implosion compression process.To every kind of fluid instability problems and multicomponent compressible large distortion flow problems,which will be met in the implosion compression process of ICF,we will all use classical high order WENO schemes or design new numerical methods based on high order WENO schemes to compute them,and then compare our high order methods with the commonly used lower order methods.Our final goal is trying to develop a high accuracy applied software for the numerical simulation of ICF implosion process for serving national defense and modernization construction,which is also one of the main innovations of the dissertation.The main work in the dissertation are as follows:(1) A class of meshiess methods for heat conduction equations are presented (see Chapter 2).The methods are first successfully applied to solve two-dimension three-temperature equations which are often met in the numerical simulation of ICF.Theoretical analysis and lots of numerical simulations show that our methods are superior to the nine-point difference schemes——the most popular in domestic at present,both in the calculation accuracy and the adaptability to irregular degree of meshes.Thus it can be seen that the meshless methods not only have important practical value for solving nonlinear parabolic equations with complex geometric boundary but have broad application prospects in the researching fields of ICF numerical simulation.(2) To multicomponent compressible large distortion flows,a class of high order mixture type finite volume WENO(FV-WENO-MT) methods are developed on the quasi-conservativeγ-based model or the quasi-conservative volume-fraction model,also when solving the control equations,a clear material interface is provided for the multicomponent problems by using the level set methods or Lagrange methods(see Cheaper 7).The original work solves the not quite clear interface's problem and breaks through the second-order accuracy methods' limitation, that open a new approach for the high accuracy calculation of the high dimensional problems which with high density-ratio,strong shock,large distortion, multi-interface and very complex changing of interface topological structures.(3) With high order finite difference WENO(FD-WENO) schemes,the satisfactory results are obtained in the numerical simulation of high density-ratio Rayleigh-Taylor(RT) instability problems,laser ablative RT instability problems and high march number Richtmyer-Meshkov(RM) instability problems,which are often met in the implosion compression process of ICF.Furthermore,according the qualitative and quantitative comparison,it is observed that high order FD-WENO schemes are obviously better than the lower order schemes,such as MUSCL and PPM(see Chapter 3 and Chapter 4).It proved that applying the high order FD-WENO schemes in the numerical simulation of the implosion compression process is feasible and quite advisable.(4) Based on the summary of the interface capturing methods and the interface tracking methods of multicomponent compressible flows,three methods including volume of fluid(VOF) methods,level set methods based on FD-WENO schemes and front tracking methods are tested.Numerical results and theoretical analysis show that the first method is not very suitable and the other two are much more appropriate(see Chapter 6).Then there is a significant conclusion that we should try to avoid using VOF methods to capture interface while applying the high order FD-WENO schemes in the numerical simulation of ICF.(5) In order to avoid forming too complicated formulas in radiation hydrodynamic equations and reduce difficulties in calculation,the internal energy(but not the total energy) is usually used as an unknown function in the three-temperature energy equations.This causes the whole system of equaions not conservative, which make the classical numerical schemes for solving hyperbolic conservation laws can't be used directly here,e.g.high order FD-WENO schemes.To deal with the contradictions,in Chapter 5,two classes of high order FD-WENO methods are designed for solving the nonconservative Euler equations.The numerical experiments show that the calculation effects are good and these two classes of new methods are obviously superior to the method introduced in[29].