雙曲型守恒律的高精度數(shù)值方法研究.pdf

1、南昌航空大學(xué)碩士學(xué)位論文雙曲型守恒律的高精度數(shù)值方法研究姓名：徐沖坤申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：微分方程數(shù)值解指導(dǎo)教師：鄭華盛20070601IIABSTRACTThe high-order accuracy and high resolution numerical method for nonlinearhyperbolic conservation laws is researched in this paper. Based on

2、cell-averagedsolution reconstruction, a class of high-order accuracy and high resolution TVDconservative difference schemes is present for nonlinear hyperbolic conservation laws.Its main idea is the following. Firstly,

3、the computational interval is divided into piecesof non-overlapping sub-intervals, and then each sub-interval is further subdividedinto small-intervals according to required accuracy. To non-uniformly partition, sub-int

4、erval is subdivided into small-intervals by using Gauss-Lobatto and Gauss-Chebyshev points. Secondly, based on cell-averaged solution from these small-intervals, the approximation with high interpolation polynomial is ob

5、tained in order toreconstruct solutions at small-interval boundaries. Furthermore, to prevent oscillationsfrom the high-order interpolation, the correction is implemented by applyingrestriction function. Moreover, the ap

6、proximate Riemann solver is used to calculatenumerical flux at small-intervals boundaries, and a high-order accurate fullydiscretization method is obtained by means of high-order Runge-Kutta TVD timediscretization. Under

7、 the condition of the CFL, the non-oscillatory property of thescheme is analysed and proved. The extension to one-dimensional conservation lawssystems and multi-dimensional equation and systems is implemented. Finally, s

8、everaltypical numerical experients are given for uniformly and non-uniformly cell partitions,and the numerical results are compared to these schemes with two cell partitions. Thenumerical results verify high accuracy and