一阶迎风和二阶ENO Local Lax-Friedrich格式的修正系数研究

ON MODIFYING COEFFICIENTS OF FIRST-ORDER UPWIND SCHEME AND SECOND-ORDER ENO LOCAL LAX-FRIEDRICH SCHEME

针对一阶迎风格式和二阶ENO Local Lax-Friedrich格式,通过"修正系数"方法对它们进行修正,在不增加模板节点数的情况下,将逼近精度提高一阶,分别称为MCupwind格式和MCENOLLF格式。理论与数值模拟实验表明,修正后的格式保持了原有格式的所有优点,在最坏的情况下自动降为原格式,"修正系数"方法能在间断或激波附近引入间断解思想将会有更好的发展前景。

In this thesis,we present two new numerical methods named MCupind scheme and MCENOLLF scheme respectively. They are based on first-order upwind scheme and second-order ENO Local Lax-Friedrieh scheme respectively, by adjusting them through ＂modifying co- efficient＂ method, the approximation accuracy is heightened one order without expanding the points＇ number of the template. Theoretical anal- ysis and the value modelling indicate that the modified schemes of MC approaches hold all the desirable properties the underlying schemes possess, and can degenerate to the underlying schemes in worst situations automatically. The modifying coefficient method will have better development prospects should the thinking of interrupted solution be drawn to the interrupted place or around the shock wave.