关于一维非恒定流方程的差分格式,底摩擦项形式和数值稳定性的关系

本文分析了一维非恒定流方程的差分格式、底摩擦项形式和数值稳定性之间的各种关系,论证了:(a)在格式中加入底摩擦项并不一定提高稳定性;(b)非对称型格式和中心差分格式应采用不同形式的底摩擦项;(c)一维非恒定流方程的一阶迎风格式和矢通量分裂格式的线性稳定性条件。

On the Relations among the Difference Schemes, Bottom Friction Forms and the Numerical Stability for 1-d Unsteady Water Flow Equations

It is analysed in this paper that the relations among the difference schemes, bottom friction forms and the numerical stability for unsteady water flow eqs. The authbr showed some important results as follows: (a) the numerical stability of a difference scheme can not always be improved by introducing a bottom friction item into it; (b) the bottom friction forms for a nonsymmetric numerical scheme must be different from that for a symmetrical one; (c) the stability criteria of the upwind schemes and the flux splitting schemes for 1-d unsteady water flow eqs.