Thomas, James L.; Diskin, Boris; Brandt, Achi Textbook multigrid efficiency for the incompressible Navier-Stokes equations: High Reynolds number wakes and boundary layers. (English) Zbl 0984.76063 Comput. Fluids 30, No. 7-8, 853-874 (2001). Summary: Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier-Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the full approximation scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: entering flow, wake flow, and boundary layer flow. Textbook efficiencies, i.e., reduction of algebraic errors below discretization errors in one full multigrid cycle, are attained for second-order accurate simulations at a laminar Reynolds number of 10,000. Cited in 6 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D25 Wakes and jets Keywords:textbook multigrid efficiency; flow past finite flat plate; incompressible Navier-Stokes equations; multigrid algorithm; distributed relaxation; defect correction; entering flow; wake flow; boundary layer flow Software:CFL3D PDFBibTeX XMLCite \textit{J. L. Thomas} et al., Comput. Fluids 30, No. 7--8, 853--874 (2001; Zbl 0984.76063) Full Text: DOI References: [1] Beam, R. M.; Warming, R. F., An implicit factored scheme for the compressible Navier-Stokes equations, AIAA J, 16, 4, 393-401 (1978) · Zbl 0374.76025 [2] Pulliam TH, Steger JL. On implicit finite difference simulations of three dimensional flow. AIAA paper 78-10, 1978; Pulliam TH, Steger JL. On implicit finite difference simulations of three dimensional flow. AIAA paper 78-10, 1978 [3] Krist SL, Biedron RT, Rumsey CL. CFL3D user’s manual (version 5.0). NASA TM-1998-208444, 1998; Krist SL, Biedron RT, Rumsey CL. CFL3D user’s manual (version 5.0). NASA TM-1998-208444, 1998 [4] Brandt, A., Guide to multigrid development, Multigrid Meth, Lect Notes Math, 960, 220-312 (1982) [5] Brandt, A., (Multigrid techniques: 1984 guide with applications to fluid dynamics, Lecture notes for the computational fluid dynamics lecture series at the computational fluid dynamics lecture series at the Von-Karman Institute for fluid dynamics (1984), Weizmann Institute for Science: Weizmann Institute for Science Rehovot, Israel), 1-183 [6] Brandt A. Barriers to achieving textbook multigrid efficiency (TME) in CFD. ICASE Interim Report No. 32, NASA CR-1998-207647, 1998; updated version available as Gauss Center Report WI/GC 10, Rehovot, Israel: Weizmann Institute for Science; December 1998. p. 1-23; Brandt A. Barriers to achieving textbook multigrid efficiency (TME) in CFD. ICASE Interim Report No. 32, NASA CR-1998-207647, 1998; updated version available as Gauss Center Report WI/GC 10, Rehovot, Israel: Weizmann Institute for Science; December 1998. p. 1-23 [7] Thomas JL, Diskin B, Brandt A. Distributed relaxation and defect correction applied to the compressible Navier-Stokes equations. AIAA paper 99-3334, Proceedings of the 14th Computational Fluid Dynamics Conference, Norfolk, VA: AIAA; 1999; Thomas JL, Diskin B, Brandt A. Distributed relaxation and defect correction applied to the compressible Navier-Stokes equations. AIAA paper 99-3334, Proceedings of the 14th Computational Fluid Dynamics Conference, Norfolk, VA: AIAA; 1999 [8] Thomas JL, Bonhaus DL, Anderson WK, Rumsey CL, Biedron RT. An (( O m^2\); Thomas JL, Bonhaus DL, Anderson WK, Rumsey CL, Biedron RT. An (( O m^2\) [9] Brandt, A.; Yavneh, I., On multigrid solution of high-Reynolds incompressible entering flows, J Comput Phys, 101, 151-164 (1992) · Zbl 0757.76033 [10] Diskin B, Thomas JL. Solving upwind-biased discretizations: defect correction iterations. ICASE report 99-14, NASA CR-1999-209106, 1999; Diskin B, Thomas JL. Solving upwind-biased discretizations: defect correction iterations. ICASE report 99-14, NASA CR-1999-209106, 1999 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.