Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust‐region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.

[1]  J. S. Vrentas,et al.  Fluid mechanics of laminar liquid jets , 1967 .

[2]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[3]  Y. Fung,et al.  Flow in Locally Constricted Tubes at Low Reynolds Numbers , 1970 .

[4]  G. Stewart.  Introduction to matrix computations , 1973 .

[5]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[6]  Joe F. Thompson,et al.  Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies , 1974 .

[7]  J. Nohel,et al.  Energy methods for nonlinear hyperbolic volterra integrodifferential equations , 1979 .

[8]  David M. author-Gay.  Computing Optimal Locally Constrained Steps , 1981 .

[9]  Jorge J. Moré,et al.  Recent Developments in Algorithms and Software for Trust Region Methods , 1982, ISMP.

[10]  Richard H. Byrd,et al.  A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .

[11]  D. Sorensen.  Newton's method with a model trust region modification , 1982 .

[12]  J. R. A. Pearson,et al.  Computational Analysis of Polymer Processing , 1983 .

[13]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[14]  K. Adachi.  Calculation of strain histories in Protean coordinate systems , 1983 .

[15]  A method for the simulation of plane or axisymmetric flows of incompressible fluids based on the concept of the stream function , 1986 .

[16]  A computational method for flows of incompressible fluids based on a non conformal transformation of the physical domain , 1986 .

[17]  C. Macosko,et al.  A finite element method for liquid with memory , 1987 .

[18]  Richard H. Byrd,et al.  Approximate solution of the trust region problem by minimization over two-dimensional subspaces , 1988, Math. Program..

[19]  T. Dinh,et al.  Training multi-layered neural network with a trust-region based algorithm , 1990 .