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1、湘潭大学 博士学位论文 多介质可压缩大变形流体及辐射热传导数值模拟研究 姓名：张瑗 申请学位级别：博士 专业：计算数学 指导教师：李寿佛 20071101 ? ?(ICF)? ? ? ?Euler? ? ? ?(weighted essentially non- oscillatory scheme,?WENO)?ICF? ?ICF? ? ?WENO? ? ?WENO? ? ? ? ?WENO? ?ICF? ? ? (1)? ?ICF? ? ? ? ?ICF? (2)?-? ? ?WENO?FV-WENO-MT? ?(?Lagrange?)? ? ? ? ? ? ? ? (3)? ?WENO?
2、(?FD-WENO)?ICF? ? ?Rayleigh-Taylor?(?RT?)? ?RT? ?Richtmyer-Meshkov?(?RM? ?)? ?FD-WENO?MUSCL?PPM? ? ?FD-WENO? ? I (4)? ?FD-WENO? (volume of fl uid,?VOF)? ?FD-WENO?(level set)?(front tracking)? ? ? ?FD-WENO ?ICF?VOF? (5)? ?(?)? ? ? FD-WENO? ?Euler? ?FD-WENO ?29? ? ?WENO? ? II ABSTRACT This dissertatio
3、n is devoted to the study of two subjects which are impor- tant for the numerical simulation of implosion compression process of inertial confi nement fusion (ICF). The fi rst subject is to search for high accuracy order Eulerian methods for the numerical simulation of multicomponent compressible la
4、rge distortion fl ow problems and fl uid interface instability problems in implosion compression process, the other one is to fi nd more effi cient numerical methods for solving three-temperature radiation heat conduction equations related to the implosion compression process. We are among the fi rs
5、t 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 fl uid instability problems and multicomponent compressible large distortion fl ow problem
6、s, 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 fi nal goal is
7、 trying to develop a high accuracy applied software for the numerical sim- ulation 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 mes
8、hless methods for heat conduction equations are presented (see Chapter 2). The methods are fi rst 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 metho
9、ds are superior to the nine-point diff erence 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 eq
10、uations with complex geometric boundary but have broad application prospects in the researching fi elds of ICF numerical simulation. (2) To multicomponent compressible large distortion fl ows, a class of high order mixture type fi nite volume WENO (FV-WENO-MT) methods are devel- oped on the quasi-co
11、nservative -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 III Lagrange methods (see Cheaper 7). The original work solves the not quite cle
12、ar interfaces problem and breaks through the second-order accuracy methods limi- tation, that open a new approach for the high accuracy calculation of the high di- mensional problems which with high density-ratio, strong shock, large distortion, multi-interface and very complex changing of interface topological structures. (3) With high order fi nite diff erence WENO (FD-WENO) schemes, the sat- isfactory results are obtained in the numerical simulation of high density-ratio Rayleigh-Taylor (RT) instability problems
