A numerical approach for computing flows by local transformations and domain decomposition using an optimization algorithm

This paper presents theoretical information for numerical simulation of two- and three-dimensional flows, based on the concepts of streamlines and local transformation functions associated with domain decomposition. In this approach, in addition to the pressure, the primary unknowns are the local mapping functions between the physical sub-domains and transformed domains where the mapped streamlines are parallel straight lines. This makes it easy to handle time-dependent constitutive equations for complex fluids. To solve the governing equations that also involve compatibility equations between sub-domains, an optimization algorithm is set up in order to compute the unknowns related to the streamlines iteratively. Applications are given for two-dimensional flows between eccentric cylinders, using different constitutive equations.

[1]  K. Adachi.  A note on the calculation of strain histories in orthogonal streamline coordinate systems , 1986 .

[2]  M. Crochet,et al.  A new mixed finite element for calculating viscoelastic flow , 1987 .

[3]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[4]  J. Clermont,et al.  Three-dimensional extrudate swell experimental and numerical study of a polyethylene melt obeying a memory-integral equation , 1999 .

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

[6]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[8]  E. Mitsoulis,et al.  An efficient algorithm for strain history tracking in finite element computations of non‐Newtonian fluids with integral constitutive equations , 1990 .

[9]  Chi King Lee,et al.  Generation of quadrilateral mesh over analytical curved surfaces , 1997 .

[10]  Robert E. Smith,et al.  Algebraic grid generation , 1982 .

[11]  O. Hassager,et al.  Three-dimensional simulations of viscoelastic instability in polymeric filaments , 1999 .

[12]  Martin H. Schultz,et al.  Elliptic problem solvers , 1981 .

[13]  T. Shiojima,et al.  Three-dimensional finite-element method for extrudate swells of a maxwell fluid , 1990 .

[14]  Nhan Phan-Thien,et al.  VISCOELASTIC FLOW BETWEEN ECCENTRIC ROTATING CYLINDERS: UNSTRUCTURED CONTROL VOLUME METHOD , 1996 .

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

[16]  M. Mackley.  Fluid Mechanics of Viscoelasticity , 2000 .

[17]  N. Phan-Thien,et al.  Three-dimensional study of extrusion processes by Boundary Element Method. , 1988 .

[18]  R. Rivlin,et al.  Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects , 1976 .

[19]  D. Ingham,et al.  A Boundary Integral Equation Method for the Study of Slow Flow in Bearings With Arbitrary Geometries , 1984 .

[20]  T. P. Dinh,et al.  Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust‐region optimization algorithm , 1991 .

[21]  J Broszeit,et al.  Finite-element simulation of circulating steady flow for fluids of the memory-integral type: flow in a single-screw extruder , 1997 .

[22]  M. Greywall.  Streamwise computation of three-dimensional incompressible potential flows , 1988 .

[23]  B. Caswell.  REPORT ON THE IXTH INTERNATIONAL WORKSHOP ON NUMERICAL METHODS IN NON-NEWTONIAN FLOWS , 1996 .

[24]  A. Yassine,et al.  OPTIMIZATION METHODS FOR SOLVING NON-LINEAR EQUATIONS IN VISCOELASTIC FLOW PROBLEMS , 1999 .

[25]  A. Wachs,et al.  Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method , 2000 .

[26]  Y. Yeow,et al.  Modelling of fluid M1 using multiple-relaxation-time constitutive equations , 1990 .

[27]  Marcel Crochet,et al.  Numerical prediction of extrudate swell of a high-density polyethylene , 1992 .

[28]  R. Larson.  A critical comparison of constitutive equations for polymer melts , 1987 .