摘要
综合隐式完全平方守恒差分格式和显式瞬时平方守恒差分格式的优点,针对一类非线性发展方程构造了一种通过自动调节时间步长来保持平方守恒性的显式差分格式。它基于加小耗散的思想,但又与小耗散法有所不同。本文取的耗散项不是一般的人工耗散,而是取能够弥补由于时间离散所产生的截断误差的所谓(时间)协调耗散。因此,该格式具有较高的时间精度。在数值试验中,该类格式可取得满意的效果。
n this paper. a kind of explicit difference schemes to solve nonlinear evolution equations. Perfectly keeping the Square conservation by adjusting the time step interval, is constructed. from the comprehensive maintenance of the advantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme. The new schemes are based on the thought of adding a small dissipation, but it is different from the Small dissipation Method. The dissipative term used in the new schemes is not a simple artificial dissipative term. It is a so-called (time) consistent dissipative term that can compensate for the truncation errors from the dissociation of the time differential term. Therefore, the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests.
出处
《气象学报》
CSCD
北大核心
1995年第3期299-305,共7页
Acta Meteorologica Sinica
基金
国家科委"攀登"计划重大关键项目
关键词
变步长
显式格式
平方守恒
差分格式
发展方程
Adjustable time interval, Explicit scheme, Square conservation, Harmoninus dissipation.