Journal ArticleDOI
Iterative solution of the stream function-vorticity formulation of the stokes problem, applications to the numerical simulation of incompressible viscous flow
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TLDR
The numerical solution of the Stokes problem in its stream function-vorticity formulation by a preconditioned conjugate gradient algorithm is discussed, constructed via Fourier analysis and leads to an algorithm which is naturally suited to finite element implementations.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1991-06-01. It has received 36 citations till now. The article focuses on the topics: Stream function & Biharmonic equation.read more
Citations
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Book ChapterDOI
Finite element methods for incompressible viscous flow
Journal ArticleDOI
Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
TL;DR: This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs) and intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully non linear PDEs.
Journal ArticleDOI
A Weak Galerkin Finite Element Scheme for the Biharmonic Equations by Using Polynomials of Reduced Order
Ran Zhang,Qilong Zhai +1 more
TL;DR: This paper explores the possibility of optimal combination of polynomial spaces that minimize the number of unknowns in the numerical scheme, yet without compromising the accuracy of the numerical approximation.
Journal ArticleDOI
A review of vorticity conditions in the numerical solution of the ζ–ψ equations
TL;DR: In this paper, a review of the conditions to be imposed on the vorticity in the calculation of two-dimensional incompressible viscous flows are discussed. And a unified understanding of several available treatments for determining the correct boundary values is achieved by including in the present analysis spatial discretizations by finite differences and finite elements, coupled and uncoupled formulations of the problem as well as steady and unsteady equations.
Journal ArticleDOI
A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
TL;DR: A finite difference scheme, applicable to general irregular planar domains, to approximate the biharmonic equation and it is proved that the proposed interpolation polynomial is fourth order accurate.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Journal ArticleDOI
Numerical Methods for Nonlinear Variational Problems
Roland Glowinski,J. T. Oden +1 more
Journal ArticleDOI
Driven cavity flows by efficient numerical techniques
TL;DR: In this paper, an efficient and reliable numerical technique of high-order accuracy is presented for solving problems of steady viscous incompressible flow in the plane, and is used to obtain accurate solutions for the driven cavity.
Related Papers (5)
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U Ghia,K.N Ghia,C. T. Shin +2 more