大气波动传播问题的一种无反射数值边界格式

A Kind of Non-Reflection Numerical Boundary Scheme for the Propagation of Atmosphere Waves

根据无反射边界条件的基本原则,考虑到高阶的数值边界格式可以减小边界误差和虚假反射,利用曲线拟合中最小二乘法的思想,提出了一种高阶的光滑拟合外推边界格式(SFEBS)．因为大气运动的控制方程简化后可以归结为一个对流方程,所以作为边界格式之间的比较和检验,在一维情况下用对流方程和数值模拟中具有代表性的波包和激波作为算例,将其与传统的基于Taylor展开思想构造的边界条件(TEBS)进行了比较．计算结果表明,在高阶情况下,用SFEBS计算波动传播问题的虚假反射约为用同阶TEBS计算的 1／6,说明高阶的SFEBS可以作为一种很好的无返射数值边界格式．为今后模拟大气波动提供了一种很好的数值边界格式．

According to the fundamental principle of non-reflection boundary conditions and considering the fact that high order numerical boundary schemes can decrease the boundary error and spurious reflections, in this paper, a high order Smooth Fitting Extrapolate Boundary Scheme （SFEBS） is proposed by using the method of the least squares for data fitting. Since the governing equations for atmosphere movement can be reduced to a convective equation, so, to verify the validity of SFEBS, the propagation of one dimensional wave packet and shock governed by convective equation are simulated and compared with the boundary scheme that is based on the idea of Taylor series expansion （TEBS hereafter）. The numerical results show that, the spurious reflections that calculated by high order SFEBS is about 1/6 of that calculated by the same order TEBS. This shows that SFEBS is a better numerical boundary scheme for outflow boundary. SFEBS will be a very good numerical boundary scheme for the numerical simulation of atmosphere waves with wide spectrum.