带有干湿界面的MUSCL型有限体积法

该文采用MUSCL型非结构化网格的有限体积法模拟有干湿界面的复杂地形的非恒定流动,以Roe格式的近似Riemann解为基础,两步Runge-Kutta法提高到时间二阶精度。对底坡源项采用特征分解保证和谐性,对摩擦力源项采用半隐式格式增加格式的稳定性。采用适当的干湿界面处理技术以满足静水问题,同时对有干湿界面的复杂地形的非恒定流动达到无质量误差。通过几个经典算例,验证了本文方法的守恒性,同时具有良好的间断捕捉能力和稳定性。

一类混合MUSCL型E格式收敛性的研究

In this paper, generalized from some monotone scheme, a class of MUSCL- Type finite difference E schemes is presented. It is proved to have second order accuracy both in space and time. And applying the theory of entropy measure- valued solution, we proved the family of approximate solutions converge to the unique entropy weak l∞ -solution. Based on the character in 1-D,the convergence to the unique entropy weak l∞ -solution is proved in 2-D. Finally, we performed numerical experiments with these schemes for system of Euler equations in both 1-D and 2-D, and the results showed that these schemes had high resolution ability for shocks, rarefactions and contact discontinuities.

二维非结构网格生成及其数值模拟

提出一种二维非结构网格生成算法以及一种新的绕翼型的数值计算格式。首先,在Delaunay生成算法的框架下结合了阵面推进算法的优点,从覆盖整个计算区域的三角形着手,给出判断准则,由这些三角形的边直接生成新点,让新点与符合要求的三角形的边的两点相连构成三角形,这样生成的三角形网格具有较好的几何性质;其次,针对二维N0 0 1 2翼型跨声速绕流问题提出了一种新的计算格式。通过建立插值模板的概念,在每一个模板上运用最小二乘和MUSCL思想相结合的办法针对初始变量构造线性插值多项式,改进了原有的权系数的计算准则,将各插值多项式通过加权平均得到在整个模板集上通用的插值多项式,从而构造出高阶的有限体积格式;最后。