基于TVD思想的高阶迎风紧致格式

紧致格式具有模板紧凑、精度高的特点，然而直接应用该格式捕捉激波会产生虚假振荡。解决该问题有多种思路，本文着重研究基于TVD思想的紧致方法。首先推导了两种5阶迎风紧致格式，并采用Fourier分析比较其耗散与色散特性。然后，采用保单调保精度方法和限制器两种不同的TVD方法，进行算例验证。计算结果表明，应用TVD方法后，格式对激波、接触间断分辨率好且鲁棒性增强，但不同的TVD方法仍存在精度降低、耗散不足等问题。

High order upwind compact schemes based on TVD algorithm

Using the same stencils, the compact schemes can get higher accuracy and resolution compared to the traditional ones. But it will come in to spurious oscillations if use the compact schemes directly. There are some methods to settle this problem. We chose the TVD algorithm in the paper. Firstly, we introduced two five order upwind compact schemes and use Fourier analysis to compare their dissipation and dispersion characteristics. Secondly, we applied two different TVD methods to Euler equations. The performance of the numerical algorithm has been assessed by performing preliminary simulations on some problems, such as the oblique shock reflection problem. The algorithm applied here is proven to have good resolution properties and robust of capturing shock waves and contacts, but still has some problems of accuracy degreed and lack of dissipation.