一类TVD型的迎风紧致差分格式

A Class of Compact Upwind TVD Difference Schemes

给出一种迎风型TVD(total variation diminishing)格式的构造方法,该方法通过限制器来抑制线性紧致格式在模拟间断流场时的非物理波动,可构造出非线性TVD型紧致格式(CTVD).然后采用该法构造出了3阶和5阶的TVD型紧致格式,并通过模拟一维组合波和Riemann问题,二维激波_涡相互干扰和激波_边界层相互作用等来考察它们的性能.数值实验表明了该类格式的高阶精度和分辨率,且过间断基本无振荡.

A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in oonservation forms. Two limiters were used to prevent non-physical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property, Two compact TVD （C-TVD） schemes were tested, one is third-order acctracy, and the other is rift[h-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a two-dimensional shock-vortex intemction and a shock-boundary flow interaclion. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.