一类混合MUSCL型E格式收敛性的研究

In this paper, generalized from some monotone scheme, a class of MUSCL- Type finite difference E schemes is presented. It is proved to have second order accuracy both in space and time. And applying the theory of entropy measure- valued solution, we proved the family of approximate solutions converge to the unique entropy weak l∞ -solution. Based on the character in 1-D,the convergence to the unique entropy weak l∞ -solution is proved in 2-D. Finally, we performed numerical experiments with these schemes for system of Euler equations in both 1-D and 2-D, and the results showed that these schemes had high resolution ability for shocks, rarefactions and contact discontinuities.

非均匀等离子体中受激Raman散射非线性行为

鉴于实际中等离子体不均匀性和非周期性边界条件，建立了受激Ｒａｍａｎ散射（ＳＲＳ）和受激Ｂｒｉｌｌｏｕｒｉｎ散射（ＳＢＳ）非线性耦合模型。ＳＢＳ对ＳＲＳ的影响主要表现在两方面：１）Ｌａｎｇｍｕｉｒ波与离子声波的非线性相互作用，２）ＳＢＳ与ＳＲＳ的竞争。本文研究了离子声衰变不稳定性、离子声波对Ｌａｎｇｍｕｉｒ波的非共振散射两种非线性过程在ＳＲＳ发展过程中的作用，给出一维不均匀等离子体中ＳＲＳ发展图象。Ｌａｎｇｍｕｉｒ波向短波转换，从而被强烈阻尼是抑制ＳＲＳ的重要机制。文中给出了ＳＢＳ／ＳＲＳ耦合过程中决定ＳＲＳ行为的两个重要特征参量，即二者有效增长率之比和增长长度之比，并结合数值结果对其进行了讨论。