求解双曲型守恒律的高精度、无波动样条逼近有限体积方法

A High Order Accurate,Non-Oscillating Finite Volume Scheme Using Spline Interpolation for Solving Hyperbolic Conservation Laws

本文从三次样条逼近出发，提出了求解流体力学双曲型守恒律的一种高精度、无波动的数值方法。针对样条函数的特性，本文提出了一种新的通量限制技术，使该方法在光滑区可以达到四阶精度，在流动参数的空间分布出现拐点或极值点时分别退化为二阶或一阶精度的格式。数值实验表明，该方法对流场中的激波和接触间断有很高的分辨率，优于二阶精度的ＴＶＤ格式。

A finite volume scheme using spline interpolation for solvine hyperbolic conservation laws is proposed in this paper. On the basis of the characteristics of cubic spline functions, a new flux limiter is constructed. The present scheme is in forth order accuracy except at the points of inflection and extremes where the scheme is second order and first order accurate respectively. Numerical experiment indicates that this scheme is computationally efficient and of very high resolution to shock and contact discontinuities.