高精度两步TVD格式的构造及数值检验

Structure and numerical simulation of high order two steps scheme

摘要: 基于通量分裂的思想,利用Taylor级数理论和第二步限制器函数的控制,构造了在光滑区域空间为三阶、时间为一阶精度的高分辨率全变差递减(TVD)格式。该格式在激波过渡点降为一阶迎风格式。并从单个线形方程推广到非线性方程及方程组情形。通过几个典型算例的计算,并与二阶TVD格式作了比较,表明该方法对流场中的激波有较高的分辨率,且是无波动的。
- 航空、航天推进系统 /
- TVD格式 /
- Taylor级数 /
- 二步格式 /
- 高精度
Abstract: Basing on the flux-vector splitting,a space 3-order accuracy total variation diminishing(TVD) scheme by applying the Taylorseries theory and the control of the limiter was constructed.The scheme was 1-order in time.In the region of the shock wave the scheme changed into 1-order upwind scheme,Then the simple linear differential equation was spread nonlinear equation.It was applied in solving typical numerical experiments.The present results were compared with those results computed by the 2 nd order TVD scheme.It testifys that the scheme has high order accuracy and high resolution for shocks waves,therefore they are non-oscillatory
- aerospace propulsion system /
- total variation diminishing(TVD) /
- Taylorseries /
- two step scheme /
- high-order accuracy

[1]	陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004.
[2]	Harten A.High resolution for hyperbolic conservation laws[J].Journal of Computational Physics,1983,49(3):357-393.
[3]	Yee H C.Construction of explicit and implicit symmetric TVD scheme and their applications[J].Journal of Computational Physic,1987,68(1):151-179.
[4]	Yu Heng,Liu Yu-Ping.A second-order accurate component-wise TVD scheme for nonlinear hyperbolic conservation laws[J].Journal of Computational Physics,2001,173(1):1-6.
[5]	Levy D,Pupo G,Russo G.A fourth-order central WENO schemes for multidimensional hyperbolic systems of conservation laws[J].SIAM J Sci Comput.,2002,24(2):480-506.
[6]	楼建锋,于恒.CTVD格式数值计算非均质炸药爆轰问题[J].计算物理,2005,22(4):358-364.Lou Jian-feng,Yu Heng.Numerical simulations of detonation in heterogeneous explosives in a CTVD scheme[J].Chinese Journal of Computational Physics,2005,22(4):358-364.
[7]	Anderson Kyle W,James L T.Comparison of finite volume flux vector splitting for the euler equations[J].AIAA Journal,1986,24(9):1453-1460.