A study on the accuracy of finite volume numerical models with non-rectangular mesh

Document Type : Article

Authors

1 Department of Water and Environmental Engineering, Shahid Beheshti University, East Vafadar Blvd., Tehranpars, Tehran, P.O. Box 1658953571, Iran

2 Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, P.O. Box 1591634311, Iran

Abstract

During numerical simulation of complex geometries and flow depth variations, non-rectangular computational cells are to be generated. However, application of this kind of mesh cause numerical errors.
A 3-D model, which was verified and validated before, was used to illustrate the problem in a simple open channel flow. A zigzag computational mesh was used to study the effect of non-rectangular cells on the accuracy of the model. Results showed that water surface and velocity profiles oscillated around the correct answer. Investigating the reason for this oscillation showed that assuming constant velocity at non-rectangular computational cell surfaces, which is a usual practice in all numerical schemes, cause this error. Variation of velocity at mesh surfaces was then added to the computation model and as a result, the oscillations in velocity profiles and water surface were eliminated. Further analysis showed that this is a general problem in any finite volume model with non-rectangular mesh.

Keywords


[1]     Vreugdenhil C.B., Wijbenga J., “Computation of flow pattern in rivers”, ASCE J. Hydraul. Div. 108 (11) (1982) 1296-1310.
[2]     Keller R.J., Rodi W., “Prediction of flow characteristics in main channel/flood plain flows”, J. Hydraul. Res. 26 (4) (1988) 425-441.
[3]     Lai C.J., Yen C.W., “Turbulent free surface flow simulation using a multi-layer model”, Int. J. Numer. Methods Fluids 16 (1993) 1007-1025.
[4]     Li C.W., Yu T.S., “Numerical investigation of turbulent shallow recirculating flows by a quasi-three-dimensional  model”, Int. J. Numer. Methods Fluids 23 (1996) 485-501.
[5]     Ye J., McCorquodale J.A., “Depth averaged hydrodynamic model in curvilinear collocated grid”, ASCE J. Hydraul. Eng. 123 (5) (1997) 380-388.
[6]     Shankar N.J., Chan E.S., Zhang Q.Y., “Three-dimensional numerical simulation for an open channel flow with a constriction”, J. Hydraul. Res. 39 (2) (2001) 187-201.
[7]     Shao X., Wang H., Chen Z., “Numerical modeling of turbulent flow in curved channels of compound cross-section”, Adv. Water Resour. 26 (5) (2003) 525-539.
[8]     Gholami A., Akhtati A.A., Minatour Y., Bonakdary H., Javadi A.A., “Experimental and numerical study on velocity field and water surface profile in a strongly-curved 90º open channel bend”, J. Eng. Appl. Comput. Fluid Mech. 8(3) (2014) 447-461.
[9]     Yoshioka H., Unami K., Fujihara M., “A dual finite volume method scheme for catastrophic flash floods in channel networks”, Appl. Math. Model. 39(1) (2015) 205-229.
[10] Zahraeifard V., Talebbeydokhti N., “Numerical simulation of turbulent flow over labyrinth spillways/weirs and corresponding discharge coefficient and efficiency”, Scientia Iranica A 22(5) (2015) 1734-1741.
[11]           Gholami A., Bonakdari H., Akhtari A.A., Ebtehaj I., “A combination of computational fluid dynamics, artificial neural network and support vectors machines model to predict flow variables in curved channel”, Scientia Iranica A 26(2) (2019) 726-741.
[12]           Rezaei B., Amiri H., “Numerical modeling of flow field in compound channels with non-prismatic floodplains”, Scientia Iranica A 25(5) (2018) 2413-2424.
[13]           Tay M.T.W., Mitchell S.B., Chen J., Williams J., “Numerical modelling approach for the management of seasonal influenced river channel entrance”, Ocean Coast. Manag. 130 (2016) 79-94.
[14] Langendoen E.J., Mendoza A., Abad J.D., et al., “Improved numerical modeling of morphodynamics of rivers with steep banks”, Adv. Water Resour. Part A 93 (2016) 4-14.
[15]           Farmani S., Barani G., Ghaeini-Hessaroeyeh M., Memarzadeh R., “Numerical modeling of flood waves in a bumpy channel with the different boundary conditions”, Scientia Iranica A 26(2) (2019) 667-677.
[16] Peric M., Analysis of pressure velocity coupling on non-orthogonal grids, Numer. Heat Transfer, Part B 17 (1990) 63-82.
[17] Zarrati A. R., Jin Y.C., “Development of a generalized multi-layer model for 3-D simulation of free surface flows”, Int. J. Numer. Methods Fluids 46 (2004) 1049-1067.
[18] An H., Yu S., “Finite volume integrated surface-subsurface flow modeling on nonorthogonal grids”, Water Resour. Res. 50 (2014) 2312-2328.
[19] Buitrago S., Sosa G., Jime╠Źnez O., “An upwind finite volume method on non-orthogonal quadrilateral meshes for the convection diffusion equation in porous media”, Appl. Anal. 95 (10) (2016) 2203-2223.
[20] Shaw J., Weller H., Methven J., Davies T., “Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes”, J. Comput. Phys. 344 (2017) 86-107.
[21] Li Y.S., Zhan J.M., “An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows”, Int. J. Numer. Methods Fluids 16 (1993) 187-198.
[22] Kim C.K., Lee J.S., “A three-dimensional PC-based hydrodynamic model using an ADI scheme”, Coast. Eng. 23 (1994) 271-287.
[23] Kodama T., Wang S.S.Y., Kawahara M., “Model verification on 3D tidal current analysis in Tokyo bay”, Int. J. Numer. Methods Fluids 22 (1996) 43-66.
[24] Wei O.W. H., Lu Q., Li Y.S., “Multi-layer modeling of three-dimensional hydrodynamic transport processes”, J. Hydraul. Res. 34 (5) (1997) 677-693.
[25] Reggio M., Hess A., Ilinca A., “3-D multiple-level simulation of free surface flows”, J. Hydraul. Res. 40 (4) (2002) 413-423.
[26] Vreugdenhil C.B., Numerical Methods for Shallow Water Flows, Kluwer Academic Publishers, Dordrecht, 1994.
[27] Patankar S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing corp., Washington, D.C., 1980.
[28] Weerakoon S.B., Tamai N., Kawahara Y., “A depth correction equation for depth-averaged flow computations in natural rivers”, Proceedings of the Environmental Hydraulics Conference, Hong Kong, 1991.
[29] Zhou J.G., “Velocity-depth coupling in shallow water flows”, ASCE J. Hydraul. Eng. 121 (10) (1995) 717-724.