Nonhydrostatic Three-Dimensional Model for Hydraulic Flow Simulation. I: Formulation and Verification
Publication: Journal of Hydraulic Engineering
Volume 129, Issue 3
Abstract
A three-dimensional numerical method, without the hydrostatic assumption, is developed to solve flow problems in hydraulic engineering. This method adopts an unstructured grid technology that is applicable to arbitrarily shaped cells and offers the potential to unify many grid topologies into a single formulation. It solves the three-dimensional turbulent flow equations and utilizes a collocated and cell-centered storage scheme with a finite-volume discretization. In Part I, the technical details of the method are presented, along with its verification and validation by computing a benchmark open channel flow. Meshes of hexahedral, tetrahedral, and prismatic shapes are employed, and results are compared with experimental data and among different meshes. Accuracy estimates and error analyses are also developed and discussed. Our companion paper applies the method to two practical problems: Flow in a hydroturbine draft tube, and flow in the forebay of Rocky Reach Dam for design of a fish passage facility.
Get full access to this article
View all available purchase options and get full access to this article.
References
Baker, T. J. (1996). “Discretization of Navier–Stokes equations and mesh-induced errors.” Proc., 5th Int. Conf. Numerical Grid Generation in Computational Field Simulation, Mississippi State Univ., Mississippi.
Barth, T. (1991). “A three-dimensional upwind Euler solver for unstructured meshes.” AIAA Pap.
Behr, M., and Tezduyar, T. E.(1994). “Finite-element solution strategies for large-scale simulations.” Comput. Methods Appl. Mech. Eng., 112, 3–24.
Berger, R. C., and Stockstill, R. L. (1999). “A finite-element system for flows.” Proc., 1999 American Society of Civil Engineers (ASCE) Water Resources Engineering Conf., Water Resources into the New Millenium, Past Accomplishments and New Challenges, Seattle.
Bernard, R. S., and Berger, R. C. (1999). “A parallel coupling scheme for disparate flow solvers.” Department of Defense High Performance Computing Modernization Program, 1999 Users Group Conference, June 1–10, Monterey, Calif.
Casulli, V.(1997). “Numerical simulation of three-dimensional free-surface flow in isopycnal coordinates.” Int. J. Numer. Methods Fluids, 25, 645–658.
Coirier, W. J., and Powell, K. G. (1995). “A Cartesian, cell-based approach for adaptively refined solutions of the Euler and Navier–Stokes equations.” AIAA Pap.
Cokljat, D., and Younis, B. A.(1995). “Second-order closure study of open-channel flows.” J. Hydraul. Eng., 121(2), 94–107.
Demuren, A. O.(1993). “A numerical model for flow in meandering channels with natural bed topography.” Water Resour. Res., 19(4), 1269–1277.
Eca, L., and Hoekstra, M. (2000). “On the application of verification procedures in computational fluid dynamics.” Proc., 2nd MARNET Workshop, Barcelona, Spain.
Ferziger, J. H., and Peric, M. (1999). “Finite difference methods.” Computational methods for fluid dynamics, Springer, New York, 59–60.
Frink, N. T.(1998). “Tetrahedral unstructured Navier–Stokes method for turbulent flows.” AIAA J., 36(11), 1975–1982.
Haselbacher, A., McGuirk, J. J., and Page, G. J.(1999). “Finite volume discretization aspects for viscous flows on mixed unstructured grids.” AIAA J., 37(2), 177–184.
Huang, J. C., and Weber, L. J. (1998). “Numerical simulation of the forebay of Lower Granite lock and dam.” Hydro Vision 98, Reno, Nev., July.
Huang, J. C. (2000). “Development and validation of a three-dimensional numerical model for application to river flows.” PhD thesis, Civil and Environmental Engineering, The University of Iowa, Iowa.
Jameson, A., Baker, T. J., and Weatherill, N. P. (1986). “Calculation of inviscid transonic flow over a complete aircraft.” AIAA Pap.
Kim, S. E., Mathur, S. R., Murthy, J. Y., and Choudhury, D. (1998). “A Reynolds-averaged Navier–Stokes solver using unstructured mesh-based finite-volume scheme.” AIAA Pap.
Lai, Y. G., So, R. M. C., and Przekwas, A. J.(1995). “Turbulent transonic flow simulation using a pressure-based method.” Int. J. Eng. Sci., 33(4), 469–483.
Lai, Y. G., and Przekwas, A. J.(1996). “A multigrid algorithm for a multiblock pressure-based flow and heat transfer solver.” Numer. Heat Transfer, Part B, 30, 239–254.
Lai, Y. G.(1997). “An unstructured grid method for a pressure-based flow and heat transfer solver.” Numer. Heat Transfer, Part B, 32, 267–281.
Lai, Y. G.(2000). “Unstructured grid arbitrarily shaped element method for fluid flow simulation.” AIAA J., 38(12), 2246–2252.
Lai, Y. G., Weber, L. J., and Moedinger, J. (2001a). “A three-dimensional unsteady method for simulating river flows.” Proc., ASCE World Water and Environmental Resource Congress, Orlando, May 20–24.
Lai, Y. G., Lin, C.-L., and Huang, J.(2001b). “Accuracy and efficiency study of lattice Boltzmann method for steady-state flow simulations.” Numer. Heat Transfer, Part B, 39, 21–43.
Lai, Y. G., Weber, L. J., and Patel, V. C.(2003). “Nonhydrostatic three-dimensional method for hydraulic flow simulation. II: Formulation and verification.” J. Hydraul. Eng., 129(3), 206–214.
Launder, B. E., and Spalding, D. B.(1974). “The numerical computation of turbulent flows.” Comput. Methods Appl. Mech. Eng., 3, 269–289.
Lohner, R., Morgan, K., Peraire, J., and Vahdati, M.(1987). “Finite-element flux-corrected transport for the Euler and Navier–Stokes equations.” Comput. Methods Appl. Mech. Eng., 7, 1093–1109.
Meselhe, E. A., and Weber, L. J. (1997). “Validation of a three-dimensional model using field measurements in a large scale river reach.” Proc., 27th Congress of the IAHR, Theme B, Vol. 2, pp. 827–832.
Meselhe, E. A., and Sotiropoulos, F.(2000). “Three-dimensional numerical model for open channels with free surface variations.” J. Hydraul. Res., 38(2), 115–121.
Patankar, S. V. (1980). Numerical heat transfer and fluid flow, McGraw–Hill, New York.
Peric, M., Kessler, R., and Scheuerer, G.(1988). “Comparison of finite volume numerical methods with staggered and collocated grids.” Comput. Fluids, 16(4), 389–403.
Rhie, C. M., and Chow, W. L.(1983). “Numerical study of the turbulent flow past an airfoil with trailing edge separation.” AIAA J., 21(11), 1526–1532.
Sinha, S. K. (1996). “Three-dimensional numerical model for turbulent flows through natural river reaches.” PhD thesis, Civil and Environmental Engineering, The University of Iowa, Iowa.
Sotiropoulos, F., and Patel, V. C. (1992). “Flow in curved ducts of varying cross section.” IIHR Report No. 358, Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa.
Thompson J. F., Warsi, Z. U. A., and Mastin, C. W. (1985). Numerical grid generation: Foundations and applications, North–Holland, New York.
Ward, S., and Kallinderis, Y. (1993). “Hybrid prismatic tetrahedral grid generation for complex 3D geometries.” AIAA Pap.
Ye, J., and McCorquodale, J. A.(1998). “Simulation of curved open channel flows by 3D hydrodynamic model.” J. Hydraul. Eng., 124(7), 687–698.
Yen, B. C. (1965). “Characteristics of subcritical flow in a meandering channel.” PhD thesis, Department of Mechanics and Hydraulics, The University of Iowa, Iowa.
Yost, S. (1995). “Three-dimensional nonhydrostatic modeling of free surface flows and transport of cohesive sediment.” PhD thesis, Civil Engineering, University of Michigan, Ann Arbor, Mich.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 129 • Issue 3 • March 2003
Pages: 196 - 205
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Jun 5, 2001
Accepted: Sep 5, 2002
Published online: Feb 14, 2003
Published in print: Mar 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.