一阶迎风格式和二阶ENO Local Lax-Friedrich格式修正系数研究

针对一阶迎风格式和二阶ENO Local Lax-Friedrich格式,通过修正系数法对其进行修正,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,修正系数法若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。

Study on the Upwind Scheme and ENO Local Lax-Friedrich Scheme's Correction Coefficients

In this paper, two new numerical methods named MCupwind and MCENOLLF, and their applications in the simulation of Rayleigh-Taylor instability i n two-phase fluid dynamics are reviewed. The MCupwind and MCENOLLF are, respectively, developed from the first-order upwind scheme and the second-order ENO Local Lax-Friedrich scheme without expanding the stencil, but with a variable coefficient in the respective schemes. Theoretical analysis and the numerical modeling indicate that the MC approach possesses the desirable properties of the original scheme, and degenerates to the original scheme in bad conditions, The correction coefficient method will be more promising if some jump can be introduced in the solution in some place, especialy near the shock wave.