高超声速复杂流动中的限制器效应数值仿真

从理论分析和数值计算两个方面，对计算流体动力学(CFD)计算中常见的几种MUSCL型迎风式限制器耗散特性进行了研究，包括superbee限制器、van Albada限制器和两种minmod限制器。首先从理论上证明minmod限制器可以是耗散性较小的压缩型限制器，前人关于minmod限制器完全是耗散型限制器的认识是不准确的。其次，通过NACA0012翼型绕流计算表明，限制器耗散特性会对数值计算收敛过程产生重要影响，耗散性越小，如superbee限制器，则收敛越困难。第三，通过一个有实验结果的24°压缩拐角高超声速复杂流动数值计算，进一步澄清了前人关于minmod限制器耗散特性的不准确认识，得到了与理论分析相一致的计算结果，即 minmod 限制器可以是耗散性比Albada限制器更小的压缩型限制器。计算结果表明，对于包含强激波的高超声速复杂流动，本文使用的minmod限制器比superbee限制器和van Albada限制器更容易满足稳定性和高精度的计算要求。

Numerical Simulations of Limiter Function Effects for Hypersonic Complex Viscous Flows

The diffusion properties of several MUSCL type (Monotone Upstream Centred Schemes for Conservation Laws) limiters including superbee limiter, van Albada limiter and two types of minmod limiters(named minmod 1 limiter and minmod 2 limiter respectively) have been studied. The theoretical analysis is performed firstly, and the results show the minmod 2 limiter, which has been mistaken as a diffusion limiter previously, is a compression limiter with some special parameters. The inaccurate impression about the minmod 2 limiter’s property is redressed. The transonic flow about NACA0012 airfoil is computed, and the results show that the diffusion property of limiter can have great influence on the convergence property of a simulation. More less the diffusion of a limiter is, such as superbee limiter, more difficult the convergence of computation is. Numerical computations of the hypersonic complex flow about a 24 degrees of compression corner is performed and experimental data are used to validate the properties of the selected limiters for hypersonic complex flows. The computational results indicate that minmod 2 limiter is a compression limiter surely, which is consistent with the theoretical analysis. For hypersonic complex flows with strong shock waves, it is recommended to use the compressive minmod 2 limiter because of its stability and high resolution.