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Numerical stability of a fixed point iterative method to determine patterns of turbulent flow in a rectangular cavity with different aspect ratios

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Bibliographic Details
Title: Numerical stability of a fixed point iterative method to determine patterns of turbulent flow in a rectangular cavity with different aspect ratios
Authors: Bermúdez, B., Rangel-Huerta, A., Alanís, D., Guerrero S., W. Fermín
Publisher Information: CIMNE
Publication Year: 2017
Collection: Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge
Subject Terms: Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits, Finite element method, Coupled problems (Complex systems) -- Numerical solutions, Navier-Stokes equations, Stream Function-vorticity formulation, Velocity- vorticity formulation, fixed point iterative method, Elements finits, Mètode dels
Description: 2D isothermal viscous incompressible flows are presented from the Navier- Stokes equations in the Stream function-vorticity formulation and in the velocity-vorticity formulation. The simulation is made using a numerical method based on a fixed point it- erative process to solve the nonlinear elliptic system that results after time discretization. The iterative process leads us to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems from which efficient solvers exist regardless of the space discretiza- tion. The experiments take place on the lid driven cavity problem for Reynolds numbers up to Re = 10000 and different aspect ratios A (A=ratio of the height to the width) A = 1 and A /= 1 such aAs = 1/2, till A = 3. It appears that with velocity and vorticity variables is more difficult to solve this kind of flows, at least with a numerical procedure similar to the one applied in stream function and vorticity variables to solve an analogous nonlinear elliptic system. To obtain such flows is not an easy task, especially with the velocity-vorticity formulation. We report here results for moderate Reynolds numbers (Re 10000), although with them enough effectiveness is achieved to be able to vary the aspect ratio of the cavity A, which causes the flow to be more unstable. Con- tribution in this work is to consider rectangular cavities of drag, which can impact on isothermal turbulent flow patterns. Another contribution is to include a wide region of the Reynolds number as well as different aspect ratios where we tested stability of the numerical scheme.
Document Type: conference object
File Description: 12 p.; application/pdf
Language: English
Relation: http://hdl.handle.net/2117/190973
Availability: http://hdl.handle.net/2117/190973
Rights: Open Access
Accession Number: edsbas.4D97CEC6
Database: BASE
Description
Abstract:2D isothermal viscous incompressible flows are presented from the Navier- Stokes equations in the Stream function-vorticity formulation and in the velocity-vorticity formulation. The simulation is made using a numerical method based on a fixed point it- erative process to solve the nonlinear elliptic system that results after time discretization. The iterative process leads us to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems from which efficient solvers exist regardless of the space discretiza- tion. The experiments take place on the lid driven cavity problem for Reynolds numbers up to Re = 10000 and different aspect ratios A (A=ratio of the height to the width) A = 1 and A /= 1 such aAs = 1/2, till A = 3. It appears that with velocity and vorticity variables is more difficult to solve this kind of flows, at least with a numerical procedure similar to the one applied in stream function and vorticity variables to solve an analogous nonlinear elliptic system. To obtain such flows is not an easy task, especially with the velocity-vorticity formulation. We report here results for moderate Reynolds numbers (Re 10000), although with them enough effectiveness is achieved to be able to vary the aspect ratio of the cavity A, which causes the flow to be more unstable. Con- tribution in this work is to consider rectangular cavities of drag, which can impact on isothermal turbulent flow patterns. Another contribution is to include a wide region of the Reynolds number as well as different aspect ratios where we tested stability of the numerical scheme.