×

zbMATH — the first resource for mathematics

A second-order time-accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids. (English) Zbl 0985.76060
From the summary: We present a second-order time-accurate fractional step method for solving unsteady incompressible Navier-Stokes equations on hybrid unstructured grids. A nonstaggered grid method is employed to enforce mass conservation on hybrid unstructured grids. The pressure and Cartesian veiocity components are defined at the center of each cell, while the face-normal velocities are defined at the mid-points of the corresponding cell faces. A second-order fully implicit time-advancement scheme is used for time integration, and the resulting nonlinear equations are linearized without losing the overall time accuracy. Both momentum and Poisson equations are integrated with finite volume method, and flow variables at the cell face are obtained using an interpolation scheme independent of cell shape. The numerical method is applied to four different benchmark problems, and proves to be accurate and efficient.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kim, J.; Moin, P., Application of a fractional-step method to incompressible navier – stokes equations, J. comput. phys., 59, 308, (1985) · Zbl 0582.76038
[2] Rhie, C.M.; Chow, W.L., Numerical study of the turbulent flow past an airfoil with trailing edge separation, Aiaa j., 21, 1525, (1983) · Zbl 0528.76044
[3] Zang, Y.; Street, R.L.; Koseff, J.R., A non-staggered grid, fractional step method for time-dependent incompressible navier – stokes equations in curvilinear coordinates, J. comput. phys., 114, 18, (1994) · Zbl 0809.76069
[4] Davidson, L., A pressure correction method for unstructured meshes with arbitrary control volumes, Int. J. numer. methods fluids, 22, 265, (1996) · Zbl 0863.76050
[5] Mathur, S.R.; Murthy, J.Y., A pressure-based method for unstructured meshes, Numer. heat transfer part B, 31, 195, (1997)
[6] Lai, Y.G., An unstructured grid method for a pressure-based flow and heat transfer solver, Numer. heat transfer part B, 32, 267, (1997)
[7] Thomadakis, M.; Leschziner, M., A pressure-correction method for the solution of incompressible viscous flows on unstructured grids, Int. J. numer. methods fluids, 22, 581, (1996) · Zbl 0865.76069
[8] Taniguchi, N.; Kobayashi, T., Finite volume method on the unstructured grid system, Comput. fluids, 19, 287, (1991) · Zbl 0732.76064
[9] Hwang, Y.-H., Calculations of incompressible flow on a staggered triangular grid, part I: mathematical formulation, Numer. heat transfer part B, 27, 323, (1995)
[10] Hwang, Y.-H., Stability and accuracy analyses for the incompressible Navier-Stokes equations on the staggered triangular grid, Numer. heat transfer part B, 32, 321, (1997)
[11] Kobayashi, M.H.; Pereira, J.M.C.; Pereira, J.C.F., A conservative finite-volume second-order-accurate projection method on hybrid unstructured grids, J. comput. phys., 150, 40, (1999) · Zbl 0934.76049
[12] Miller, J.J.H.; Wang, S., An exponentially fitted finite volume method for the numerical solution of 2D unsteady incompressible flow problems, J. comput. phys., 115, 56, (1994) · Zbl 0810.76064
[13] Pan, D.; Lu, C.-H.; Cheng, J.-C., Incompressible flow solution on unstructured triangular meshes, Numer. heat transfer part B, 26, 207, (1994)
[14] Weiss, J.M.; Smith, W.A., Preconditioning applied to variable and constant density flows, Aiaa j., 33, 2050, (1995) · Zbl 0849.76072
[15] Schulz, K.W.; Kallinderis, Y., Unsteady flow structure interaction for incompressible flows using deformable hybrid grids, J. comput. phys., 143, 569, (1998) · Zbl 0935.76052
[16] Chen, A.J.; Kallinderis, Y., Adaptive hybrid (prismatic-tetrahedral) grid for incompressible flows, Int. J. numer. methods fluids, 26, 1085, (1998) · Zbl 0912.76050
[17] Hall, C.A.; Cavendish, J.C.; Frey, W.H., The dual variable method for solving fluid flow difference equations on Delaunay triangulations, Comput. fluids, 20, 145, (1991) · Zbl 0729.76047
[18] Chou, S.H., Analysis and convergence of a covolume method for the generalized Stokes problem, Math. comput., 66, 85, (1997) · Zbl 0854.65091
[19] B. Perot, Conservation properties of unstructured staggered mesh schemes, J. Comput. Phys, to appear. · Zbl 0972.76068
[20] Nicolaides, R.A., Direct discretization of planar div-curl problems, SIAM J. numer. anal., 29, 32, (1992) · Zbl 0745.65063
[21] Le, H.; Moin, P., An improvement of fractional step methods for the incompressible Navier-Stokes equations, J. comput. phys., 92, 369, (1991) · Zbl 0709.76030
[22] Choi, H.; Moin, P., Effects of the computational time step on numerical solutions of turbulent flow, J. comput. phys., 113, 1, (1994) · Zbl 0807.76051
[23] Beam, R.M.; Warming, R.F., An implicit factored scheme for the compressible Navier-Stokes equations, Aiaa j., 16, 393, (1978) · Zbl 0374.76025
[24] Choi, H.; Moin, P.; Kim, J., Direct numerical simulation of turbulent flow over riblets, J. fluid mech., 255, 503, (1993) · Zbl 0800.76296
[25] Thompson, J.F.; Warsi, Z.U.A.; Mastin, C.W., Numerical grid generation, (1985) · Zbl 0598.65086
[26] Barrett, R.; Berry, M.; Chan, T.F.; Demmel, J.; Donato, J.M.; Dongarra, J.; Eijkhout, V.; Pozo, R.; Romine, C.; der Vorst, H.V., Templates for the solution of linear systems: building blocks for iterative methods, (1994)
[27] Ghia, U.; Ghia, K.N.; Shin, C.T., High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. comput. phys., 48, 387, (1982) · Zbl 0511.76031
[28] Pauley, L.L.; Moin, P.; Reynolds, W.C., The structure of two-dimensional separation, J. fluid mech., 220, 397, (1990)
[29] Armaly, B.F.; Durst, F.; Pereira, J.C.F.; Schönung, B., Experimental and theoretical investigation of backward-facing step flow, J. fluid mech., 127, 473, (1983)
[30] Park, J.; Kwon, K.; Choi, H., Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160, KSME int. J., 12, 1200, (1998)
[31] Fey, U.; König, M.; Eckelmann, H., A new Strouhal-Reynolds-number relationship for the circular cylinder in the range 47<re<2×10^{5}, Phys. fluids, 10, 1547, (1998)
[32] Pirzadeh, S., Structured background grids for generation of unstructured grids by advancing-front method, Aiaa j., 31, 257, (1993)
[33] Williamson, C.H.K., Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers, J. fluid mech., 206, 579, (1989)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.