【作者】 毕鸿戈；

【导师】 冯国泰；

【作者基本信息】 哈尔滨工业大学 ， 动力机械及工程， 2007， 硕士

【摘要】 为了在众多的差分格式中筛选出具有较高的计算精度同时兼顾较高计算效率的差分格式,本文对一些著名的格式进行了比较分析。首先介绍了模型方程的一个可允许弱解,利用经典格式、一阶TVD格式、Harten格式、Godunov格式、二阶Godunov格式(MUSCL方法)和三阶Godunov格式(PPM方法)对模型方程进行求解,又介绍了欧拉方程Riemann问题解类型的判断规则及求解方法,用Roe格式、Harten格式、AUSM格式求解欧拉方程激波管问题,最后用Crank-Nicolson半隐格式和高精度全隐紧致格式求解线性Burgers方程。利用Fortran95中的cpu-time函数在单任务状态下计算上述差分格式的计算时间,分析计算效率。经过算例检验证实:在对模型方程的求解中,三阶Godunov格式(PPM方法)具有较高的计算精度及计算效率。在对欧拉方程的求解中,AUSM格式虽然具有计算速度快的特点,但仅具有一阶精度。在对线性Burgers方程的求解中,高精度全隐紧致格式在空间上达到四阶精度,同时又保持了较高的计算效率。更多还原

【Abstract】 For the sake of seeking an scheme with both accuracy and efficiency, this article compare and analyze some famous schemes. Firstly, this article introduces a permissible weak solution, use classical schemes、first order TVD scheme、Harten scheme、Godunov scheme、second order Godunov scheme(MUSCL method) and third order Godunov scheme(PPM method) to solve model equation. Secondly, this article introduces the regulation of how to judge the type of Riemann solution and the method of how to solve, use Roe scheme、Harten scheme and AUSM scheme to solve the shock tube problem of Euler equation. Finally, this article use Crank-Nicolson scheme、High-Order compact implicit difference method to solve linear Burgers equation and use the cpu-time function provided by Fortran95 to test the efficiency of above schemes. Numerical results prove: When solve the model equation, third order Godunov scheme (PPM method) is more accurate and efficient than other schemes, When solve the Euler equation, although AUSM scheme’s computational speed is fast, the scheme only have first order accuracy, When solve the linear Burgers equation, High-Order compact implicit difference method have forth order in space and high efficiency.更多还原