TY - JOUR

T1 - Construction of solution curves for large two-dimensional problems of steady-state flows of incompressible fluids

AU - De Almeida, V. F.

AU - Derby, J. J.

PY - 2000

Y1 - 2000

N2 - This work represents a step toward advancing classical methods of bifurcation analysis in conjunction with very large-scale scientific computing needed to model realistically processes which involve laminar and steady flows of incompressible fluids. A robust method of analysis based on pseudoarclength continuation, Newton's method, and direct solution of linear systems is proposed and applied to the analysis of a representative system of fluid mechanics, namely the tilted lid driven cavity. Accurate solution curves, possessing simple singular points, were computed for Reynolds numbers varying from 0 to 10,000 and for different angles of tilt. The results demonstrate that two-dimensional models with up to 1,000,000 algebraic equations can be studied feasibly using the methods described here with state-of-the-art vector supercomputers.

AB - This work represents a step toward advancing classical methods of bifurcation analysis in conjunction with very large-scale scientific computing needed to model realistically processes which involve laminar and steady flows of incompressible fluids. A robust method of analysis based on pseudoarclength continuation, Newton's method, and direct solution of linear systems is proposed and applied to the analysis of a representative system of fluid mechanics, namely the tilted lid driven cavity. Accurate solution curves, possessing simple singular points, were computed for Reynolds numbers varying from 0 to 10,000 and for different angles of tilt. The results demonstrate that two-dimensional models with up to 1,000,000 algebraic equations can be studied feasibly using the methods described here with state-of-the-art vector supercomputers.

KW - Factorization of large unsymmetric sparse matrices

KW - Incompressible and viscous fluids

KW - Lid driven cavity

KW - Navier-Stokes equations

KW - Parameter continuation

KW - Path following

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U2 - 10.1137/S1064827598334514

DO - 10.1137/S1064827598334514

M3 - Article

AN - SCOPUS:0034455362

SN - 0036-1445

VL - 22

SP - 285

EP - 311

JO - SIAM Review

JF - SIAM Review

IS - 1

ER -