Implicit boundary conditions for coupled solvers

Abstract In addition to implicitly resolving the velocity pressure coupling at interior faces, it is also critical for a coupled solver to implicitly resolve this coupling for boundary faces. Failure to account for this leads to substantial degradation in the convergence characteristics of the solver. In this paper, details on the implicit treatment of boundary conditions for a coupled solver are presented in the context of the OpenFOAM® framework. The boundary conditions presented include two geometric conditions namely, cyclicMMI and symmetry condition and a number of physical boundary conditions (inlet, outlet, and wall). The treatment is illustrated with modification to the boundary element coefficients and its effectiveness demonstrated for the case of “NASA Rotor 37”, a standard validation case.

[1]  C. Rhie,et al.  A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation , 1982 .

[2]  Tony Saad,et al.  Parallelization of an Additive Multigrid Solver , 2008 .

[3]  Hrvoje Jasak,et al.  Error analysis and estimation for the finite volume method with applications to fluid flows , 1996 .

[4]  F. Moukalled,et al.  Performance comparison of the NWF and DC methods for implementing High-Resolution schemes in a fully coupled incompressible flow solver , 2011, Appl. Math. Comput..

[5]  T. Gjesdal,et al.  Comparison of pressure correction smoothers for multigrid solution of incompressible flow , 1997 .

[6]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[7]  Ruey-Hor Yen,et al.  ENHANCEMENT OF THE SIMPLE ALGORITHM BY AN ADDITIONAL EXPLICIT CORRECTOR STEP , 1993 .

[8]  M. Darwish,et al.  A Fully Coupled Navier-Stokes Solver for Fluid Flow at All Speeds , 2014 .

[9]  M. Darwish,et al.  A fully coupled OpenFOAM® solver for transient incompressible turbulent flows in ALE formulation , 2017 .

[10]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[11]  M. Darwish,et al.  A Coupled Pressure-Based Finite-Volume Solver for Incompressible Two-Phase Flow , 2015 .

[12]  F. Moukalled,et al.  A coupled finite volume solver for the solution of incompressible flows on unstructured grids , 2009, J. Comput. Phys..

[13]  M. Darwish,et al.  Transient Schemes for Capturing Interfaces of Free-Surface Flows , 2012 .

[14]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[15]  S. Muzaferija,et al.  Adaptive finite volume method for flow prediction using unstructured meshes and multigrid approach , 1994 .

[16]  M. Darwish,et al.  The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab , 2015 .

[17]  J. Murthy,et al.  A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES , 1997 .

[18]  Daniel C. Asmar,et al.  A COMPARATIVE ASSESSMENT WITHIN A MULTIGRID ENVIRONMENT OF SEGREGATED PRESSURE-BASED ALGORITHMS FOR FLUID FLOW AT ALL SPEEDS , 2004 .

[19]  I. Demirdzic,et al.  Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology , 1995 .

[20]  M. Darwish,et al.  Implementation of boundary conditions in the finite-volume pressure-based method—Part I: Segregated solvers , 2016 .

[21]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[22]  M. Darwish,et al.  A pressure-based algorithm for multi-phase flow at all speeds , 2003 .

[23]  I. Demirdzic,et al.  A finite volume method for computation of fluid flow in complex geometries , 1982 .

[24]  Rodrick V. Chima SWIFT Code Assessment for Two Similar Transonic Compressors , 2009 .

[25]  M. Darwish,et al.  PRESSURE-BASED ALGORITHMS FOR MULTIFLUID FLOW AT ALL SPEEDS—PART I: MASS CONSERVATION FORMULATION , 2004 .

[26]  B. Sekar,et al.  A robust multi‐grid pressure‐based algorithm for multi‐fluid flow at all speeds , 2003 .

[27]  K. Suder Experimental Investigation of the Flow Field in a Transonic, Axial Flow Compressor with Respect to the Development of Blockage and Loss , 2013 .

[28]  M. Darwish,et al.  A Compact Procedure for Discretization of the Anisotropic Diffusion Operator , 2009 .

[29]  M. Darwish,et al.  A UNIFIED FORMULATION OF THE SEGREGATED CLASS OF ALGORITHMS FOR FLUID FLOW AT ALL SPEEDS , 2000 .

[30]  I. Demirdžić On the Discretization of the Diffusion Term in Finite-Volume Continuum Mechanics , 2015 .

[31]  M. Darwish,et al.  THE PERFORMANCE OF GEOMETRICCONSERVATION-BASED ALGORITHMS FORINCOMPRESSIBLE MULTIFLUID FLOW , 2004 .

[32]  M. Darwish,et al.  Convective Schemes for Capturing Interfaces of Free-Surface Flows on Unstructured Grids , 2006 .

[33]  M. Darwish,et al.  A high-resolution pressure-based algorithm for fluid flow at all speeds , 2001 .

[34]  D. Spalding,et al.  Two numerical methods for three-dimensional boundary layers , 1972 .

[35]  M. Darwish,et al.  An OpenFOAM pressure-based coupled CFD solver for turbulent and compressible flows in turbomachinery applications , 2016 .

[36]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[37]  M. Darwish,et al.  A Coupled Incompressible Flow Solver on Structured Grids , 2007 .