摘要
Lagrange系统下的非定常流体力学数值方法中,使用非守恒型能量方程获得的总能量(内能与动能之和)的误差大小是鉴别一种格式好坏的重要标志之一.讨论在柱坐标系下两种有限元方法的离散格式及其能量守恒性.一种是采用由因子r-1来加权插值基函数的Galerkin有限元方法,即面平均格式;另一种是直接加权插值基函数的Galerkin有限元方法,即体平均格式.误差分析表明体平均格式具有较小的能量守恒误差,数值计算结果也显示出体平均格式能量守恒误差比面平均格式明显小.
The errors of total energy (summation of internal and kinetic energy) gotten by means of non-conservation energy equation is an important criterion to a kind of hydrodynamics scheme about Lagrangian unsteady fluid. The paper discusses the way of discretization and energy conservation of two kinds of finite element methods. One Galerkin scheme which uses factor γ-1 to weigh interpolation base function, is an area average scheme. Another is Galerkin scheme which directly weigh interpolation base function, is an volume average scheme. The theoretical analysis shows that the volume average scheme has much less errors than area average one, and numerical example demonstrates this conclusion.
出处
《力学学报》
EI
CSCD
北大核心
2003年第1期69-73,共5页
Chinese Journal of Theoretical and Applied Mechanics
关键词
流体力学
LAGRANGE系统
非定常流
能量守恒
面平均格式
有限元方法
Lagrangian method, finite element scheme, non-conservation energy equation, area average scheme, volume average scheme
