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Implementing a high-order accurate implicit operator scheme for solving steady incompressible viscous flows using artificial compressibility method

Hejranfar, K ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1002/fld.2288
  3. Publisher: 2011
  4. Abstract:
  5. This paper uses a fourth-order compact finite-difference scheme for solving steady incompressible flows. The high-order compact method applied is an alternating direction implicit operator scheme, which has been used by Ekaterinaris for computing two-dimensional compressible flows. Herein, this numerical scheme is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. For space discretizing the convective fluxes, fourth-order centered spatial accuracy of the implicit operators is efficiently obtained by performing compact space differentiation in which the method uses block-tridiagonal matrix inversions. To stabilize the numerical solution, numerical dissipation terms and/or filters are used. In this study, the high-order compact implicit operator scheme is also extended for computing three-dimensional incompressible flows. The accuracy and efficiency of this high-order compact method are demonstrated for different incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid resolution and pseudocompressibility parameter on accuracy and convergence rate of the solution. The effects of filtering and numerical dissipation on the solution are also investigated. Test cases considered herein for validating the results are incompressible flows in a 2-D backward facing step, a 2-D cavity and a 3-D cavity at different flow conditions. Results obtained for these cases are in good agreement with the available numerical and experimental results. The study shows that the scheme is robust, efficient and accurate for solving incompressible flow problems
  6. Keywords:
  7. High-order accurate implicit operator scheme ; Numerical dissipation term ; Alternating direction implicit ; Artificial compressibility method ; Backward facing step ; Convective flux ; Convergence rates ; Finite-difference scheme ; Flow condition ; Fourth-order ; Grid resolution ; High-order ; Incompressible Navier Stokes equations ; Matrix inversions ; Numerical dissipation ; Numerical scheme ; Numerical solution ; Primitive variables ; Pseudo-compressibility ; Sensitivity studies ; Spatial accuracy ; Steady incompressible viscous flows ; Test case ; Compressibility ; Filtration ; Mathematical operators ; Matrix algebra ; Navier Stokes equations ; Numerical methods ; Three dimensional ; Viscous flow ; Incompressible flow
  8. Source: International Journal for Numerical Methods in Fluids ; Volume 66, Issue 8 , July , 2011 , Pages 939-962 ; 02712091 (ISSN)
  9. URL: http://onlinelibrary.wiley.com/doi/10.1002/fld.2288/abstract;jsessionid=73C2547A719F5A2ECB2177B99D473577.f03t01