高阶ENO格式应用研究

【作者】 段毅；

【导师】 杨永；

【作者基本信息】 西北工业大学 ， 流体力学， 2002， 硕士

【摘要】 本文构造了一维、二维结构网格中的高阶精度基本无振荡(ENO)有限体积格式，并且讨论了它在双曲守恒型方程中的应用。ENO格式基于近似理论，采用自适应基架技术(即自动选取所有基架中相对最为光滑的基架)，对网格平均值构造分段光滑的高阶多项式来获得高阶空间精度，同时保证格式在间断附近具有基本无振荡性质。这样，ENO格式就具有较好的激波捕捉能力。在有限体积离散中对时间的积分采用了三阶TVD Runge-Kutta时间推进格式，从而使得ENO格式可以应用于非定常流动的高阶数值模拟。文中选取了具有代表性的算例，通过求解Euler方程来验证ENO格式在处理包含激波和复杂流动结构的空气动力学问题中所具有的优点。更多还原

【Abstract】 In this paper, we develop the high-order accurate essentially non-oscillatory (ENO) schemes on one and two-dimensional structured meshes in the finite volume formulation, and discuss their applications in hyperbolic conservation laws. ENO schemes are based on the approximation theory, which achieve high-order spatial accuracy by reconstructing piecewise smooth high-order approximate polynomial from the cell-averaging values. During the reconstruction, adaptive stencil technology, which automatically chooses the relatively smoothest stencil from all possible stencils, is adopted to guarantee essentially non-oscillation near the discontinuity. Thus, the ENO schemes have better shock-capturing ability. In the finite volume discretization approach, third-order TVD Runge-Kutta time stepping scheme is applied to the time integration, which assures the ENO schemes can be used in the high-order numerical simulation of unsteady flows. The numerical examples presented here are representative test cases of the aerodynamics problems which contains shock and complicated flow structures. The solutions of Euler equations for these examples certify the advantages of ENO schemes更多还原