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A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
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2017 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 150, 84-94 p.Article in journal (Refereed) Published
Abstract [en]

Incompressible Navier-Stokes solvers based on the projection method often require an expensive numerical solution of a Poisson equation for a pressure-like variable. This often involves linear system solvers based on iterative and multigrid methods which may limit the ability to scale to large numbers of processors. The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods. Such a scheme should theoretically scale well on large numbers of CPUs, GPU'€™s, or hybrid CPU-GPU architectures. The original ACM was only valid for steady flows and dual-time stepping was often used for time-accurate simulations. Recently, Clausen [7] has proposed the entropically damped artificial compressibility (EDAC) method which is applicable to both steady and unsteady flows without the need for dual-time stepping. The EDAC scheme was successfully tested with both a finite-difference MacCormack'€™s method for the two-dimensional lid driven cavity and periodic double shear layer problem and a finite-element method for flow over a square cylinder, with scaling studies on the latter to large numbers of processors. In this study, we discretize the EDAC formulation with a new optimized high-order centered finite-difference scheme and an explicit fourth-order Runge-€“Kutta method. This is combined with an immersed boundary method to efficiently treat complex geometries and a new robust outflow boundary condition to enable higher Reynolds number simulations on truncated domains. Validation studies for the Taylor-€“Green Vortex problem and the lid driven cavity problem in both 2D and 3D are presented. An eddy viscosity subgrid-scale model is used to enable large eddy simulations for the 3D cases. Finally, an application to flow over a sphere is presented to highlight the boundary condition and performance comparisons to a traditional incompressible Navier-€“Stokes solver is shown for the 3D lid driven cavity. Overall, the combined EDAC formulation and discretization is shown to be both effective and affordable.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 150, 84-94 p.
Keyword [en]
Artificial compressibility method, EDAC, High-order numerical methods, Large Eddy simulation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-136507DOI: 10.1016/j.compfluid.2017.03.030ISI: 000401219000007OAI: oai:DiVA.org:liu-136507DiVA: diva2:1089226
Note

Funding agencies: Rosenblatt Chair within the faculty of Mechanical Engineering; Zeff Fellowship Trust

Available from: 2017-04-19 Created: 2017-04-19 Last updated: 2017-06-13Bibliographically approved

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The full text will be freely available from 2019-04-01 08:00
Available from 2019-04-01 08:00

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CiteExportLink to record
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