CTVD格式应用及相关问题研究

【作者】 黄奎邦；

【导师】 于恒；

【作者基本信息】 中国工程物理研究院 ， 流体力学， 2009， 硕士

【摘要】 本文工作分为三部分。第一部分针对磁流体力学方程组(MHD)特征异常复杂的特点,将一种无需利用雅可比矩阵对方程组进行特征解耦的格式(CTVD)推广到MHD数值模拟中。CTVD是一种具有二阶精度的TVD格式,其简单实用、无需特征解耦的特点使该格式在MHD数值模拟中具有较高的推广价值。本文采用局部的Lax-Friedrichs分裂代替CTVD格式原有的全局Lax-Friedrichs分裂,使MHD数值模拟具有更高的分辨率,在相关算例中获得了较好的结果。第二部分是将高分辨的CTVD格式应用到多介质流体力学数值模拟中,分别采用1/(γ-1)模型的守恒方法和非守恒方法。数值实验表明,即使采用守恒方法,物质界面附近的振荡是很轻微的,加密网格后,振荡基本消失。采用无振荡的TVD格式(NOS1)来处理非守恒方程后,CTVD格式成功消除物质界面附近的振荡。最后一部分内容是采用两种方法去克服HLLC Riemann近似解在二维欧拉方程中出现的激波不稳定现象。第一种方法是旋转方法,随后,借鉴了旋转方法的网格法线向量的速度差分解,得出了一个自适应的探测加权函数,进而得出HLLC组合方法。相关数值实验表明,在时间、健壮性方面,组合方法优于旋转方法,在对间断的分辨率方面,两种方法相当。更多还原

【Abstract】 The paper consists of three parts. In the first part, we present CTVD scheme as a Jacobian-free solver for ideal magnetohydrodynamics(MHD) equations which have complicated characteristics. CTVD scheme, as a second order-order scheme in space and time, avoids characteristic decomposition of the Jacobian and is efficient for MHD computations. After using local Lax-Friedrichs flux splitting instead of global Lax-Friedrichs flux splitting in Yu[25], we get more accurate numerical results in MHD computations. The results of several one-dimension and two-dimension tests demonstrate that CTVD scheme is an efficiency, and has high resolution in MHD computations.In the second part, we use high-resolution CTVD scheme to solve the Euler equations of multi-component flows. The numerical experiments of conservative CTVD scheme for the gas mixtures only produces slight oscillations near the interfaces. And the oscillations disappear when the computation is on very fine grids. We also adopt a non-oscillation TVD scheme(NOSl) to solve the non-conservative equations and the CTVD scheme eliminates the oscillations when being applied to the non-conservative equations.In the third part, we proposed two methods to cure the numerical shock instability for HLLC Riemann solver in two-dimension Euler equations. One method uses the rotated method and the other one is the hybrid method. Taking into account the efficiency, accuracy and robustness, the hybrid method is better than rotated method for HLLC solver. A series of test problems prove this conclusion.更多还原