一维高阶ENO格式的应用研究

Investigation and Application of One-Dimensional High Order ENO (Essentially Non-Oscillatory) Schemes

构造了基本 ENO有限体积格式 ,在标量守恒系 ,矢量守恒系中研究了 ENO格式的具体应用 ,给出了矢量守恒系中基于特征分量的 ENO重构算法 ,通过采用 Roe平均通量差分分裂 ( Roe-FDS) ,有效地抑制了间断解附近的振荡。一维 Euler方程的数值模拟结果进一步表明 ENO格式具有较高的激波分辨率和较低的数值耗散 。

Many high order nonlinear numerical schemes revert to first order at local extrema. Harten et al [1] developed ENO schemes by using adaptive stencil to achieve uniform high order accuracy. ENO schemes avoid a Gibbs phenomenon at discontinuities. In this paper, we discuss one dimensional finite volume ENO schemes in scalar conservation laws and system of conservation laws. Especially, we extend componentwise reconstruction to characteristic variables reconstruction in hyperbolic systems of conservation laws and avoid the more possible oscillations due to collision of discontinuities. We apply Roe averaged flux difference splitting (Roe FDS) to discretizing flux, providing ENO schemes with high resolution to capture discontinuities. We employ third order TVD Runge Kutta time stepping for time integration, thus making ENO schemes well suited to unsteady flow problems. Section 3 discusses in some detail several numerical experiments that are physically relevant and provides numerical results in Figs.1, 2a, 2b, 2c, 3a and 3b. These results demonstrate preliminarily that ENO schemes are promising as high order schemes for complicated flow simulations.