Variational Principles in Hydrodynamics of a Non-Newtonian Fluid
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摘要: 本文将钱伟长教授在文献[1]中提出的不可压缩粘性流的最大功率消耗原理进一步推广到本构方程为εij=∂τ/∂σ'ij的非牛顿流体流动问题,并采用识别的拉氏乘子法解除变分约束条件,导出其广义变分原理。Abstract: In this paper, the principle of maximum power losses for the incompressible visous fluid proposed by professor Chien Weizang in reference[1]is further extended to the hydrodynamic problem of the non-Newtonian fluid with constive law expressed as εij=∂τ/∂σ'ij. The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.
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Key words:
- non-Newtonian fluid /
- variational principle /
- Lagrangian multiplier
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[1] 钱伟长,粘性流体力学的变分原理和广义变分原理,应用数学和力学,5(3)(1984),305. [2] C.C.Lin and L.Rubinov,On the flow behind curved shocks,J.Math.Phy sics,27(1945),105. [3] V.I.Skobelkin,Variational principle in hydrodynamics,Soviet Phy sics-J ET P,4(1)(1957),68. [4] K.G.Guderly,An extremum principle for three dimensional compressible inviscid flows,SIAN,J. Appl.Math.,23(27)(1972),259. [5] A.R.Manwell,Avariational principle of steady homogenetic compressible flow with finite shocks, Wave Motion,2(1980),83. [6] M.Hafez and D.Lovell,Numerical solution of transonic stream function equation,AIAA Journal,21 (3)(1983). [7] 沈敏、孙其仁,一类非牛顿流体流动问题的变分原理和广义变分原理,应用数学和力学,16(4) (1995),345. [8] M.J.Grochet,A.R.Davis and K.Walters,Numerical Simulation of Non-Newtonian Flow,Elsevier(1984). -
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