High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
01 Dec 1982-Journal of Computational Physics (JOURNAL OF COMPUTATIONAL PHYSICS)-Vol. 48, Iss: 3, pp 387-411
TL;DR: The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions.
About: This article is published in Journal of Computational Physics.The article was published on 1982-12-01. It has received 4018 citations till now. The article focuses on the topics: Multigrid method & Rate of convergence.
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...Our review of the literature has identified a number of authors who have contributed to the verification of CFD solutions [11, 28, 33, 34, 3942, 45, 47, 49, 57, 60, 65, 74, 87-89, 92, 97, 110, 116, 117, 120, 127, 129-131, 137-139, 141, 142, 144, 147, 165, 171, 177, 209, 218, 219, 221, 228, 229, 273, 274, 277, 278, 281, 298, 306-309, 318, 325, 327, 329, 333-337, 340, 347, 350, 351, 353]....
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...Examples of benchmark PDE solutions in fluid dynamics are the following: incompressible laminar flow over a semi-infinite flat plate [87, 329, 347]; incompressible laminar flow over a parabolic plate [49, 88, 92]; incompressible laminar flow in a square cavity driven by a moving wall [34 , 130, 131, 141, 147, 228, 298, 318]; laminar nat convection in a square cavity [89, 165], incompressible laminar flow over an infinite-length circular cylinder [28, 33, 177, 218]; and incompressible laminar flow over a backward-facing step, with and without heat transfer [40, 127, 138, 142]....
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...[105] were also used by Yu et al....
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References
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TL;DR: In this paper, the boundary value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes, and interactions between these levels enable us to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); and conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "°°-order" approximations and low n, even when singularities are present.
Abstract: The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining \"°°-order\" approximations and low n, even when singularities are present. General theoretical analysis of the numerical process. Numerical experiments with linear and nonlinear, elliptic and mixed-type (transonic flow) problemsconfirm theoretical predictions. Similar techniques for initial-value problems are briefly
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