ANZIAM J. 46(E) pp.C623--C636, 2005.
Development of a 3D non-hydrostatic pressure model for free surface flows
J. W. Lee | M. D. Teubner | J. B. Nixon | P. M. Gill |
Abstract
A three-dimensional, non-hydrostatic pressure, numerical model for free surface flows is presented. By decomposing the pressure term into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step, the momentum equations are solved without the hydrostatic pressure term using Newton's method in conjunction with the generalised minimal residual (GMRES) method. This combined method does not require the determination of a Jacobian matrix explicitly but simply the product of the Jacobian and a vector, thereby reducing the amount of storage required and significantly decreasing the overall computational time required. By using Newton's method, the numerical model can handle implicitly almost all variables, unlike many other numerical models. Hence numerical stability is achieved effectively. In the second fractional step, the pressure-Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the processing time dramatically. After the new pressure field is obtained the intermediate velocities, which are calculated from the previous fractional step, are updated and then these updated velocities preserve the local mass conservation. The newly developed model is verified against analytical solutions, with good agreement.
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Authors
- J. W. Lee
- Applied Mathematics, The University of Adelaide, South Australia, Australia. mailto:jong.lee@adelaide.edu.au
- M. D. Teubner
- Applied Mathematics, The University of Adelaide, South Australia, Australia.
- J. B. Nixon
- United Water International, GPO Box 1875, South Australia, Australia.
- P. M. Gill
- Applied Mathematics, The University of Adelaide, South Australia, Australia.
Published July 12, 2005. ISSN 1446-8735
References
- P. N. Brown and Y. Saad. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 1990, 11:450--481.
- V. Casulli. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. Int. J. Numer. Meth. Fluids 1999, 30:425--440. URL
- R. G. Dean and R. A. Dalrymple. Water Wave Mechanics for Engineers and Scientists. World Scientific, 1991.
- K. A. Hoffmann and S. T. Chiang. Computational Fluid Dynamics for Engineering: Volume {II}. Engineering Education System, 1993.
- W. Huang and M. Spaulding. 3D model of estuarine circulation and water quality induced by surface discharges. J. Hydraul. Eng. 1995, 121:300--311. URL
- M. B. Kocyigit, R. A. Falconer and B. Lin. Three-dimensional numerical modelling of free surface flows with non-hydrostatic pressure. Int. J. Numer. Meth. Fluids 2002, 40:1145--1162. http://dx.doi.org/10.1002/fld.376.
- Q. Lu and O. W. H. Wai. An efficient operator splitting scheme for three-dimensional hydrodynamic computations. Int. J. Numer. Meth. Fluids 1998, 26:771--789. URL
- S. V. Patankar. Numerical Heat Transfer and Fluid Flow. McGraw Hill, 1980.
- Y. Saad. Numerical Methods for Large Eigenvalue Problems (Algorithms and Architectures for Advanced Scientific Computing). John Wiley and Sons Inc, 1992.
- G. Stelling and M. Zijlema. An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation. Int. J. Numer. Meth. Fluids 2003, 43:1--23. http://dx.doi.org/10.1002/fld.595.
- H. C. Yee. Construction of explicit and implicit symmetric TVD schemes and their applications. J. Comput. Physics 1987, 68:151--179. http://dx.doi.org/10.1016/0021-9991(87)90049-0.