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Type: Journal article
Title: A 3-D non-hydrostatic pressure model for small amplitude free surface flows
Author: Lee, J.
Teubner, M.
Nixon, J.
Gill, P.
Citation: International Journal for Numerical Methods in Fluids, 2006; 50(6):649-672
Publisher: John Wiley & Sons Ltd
Issue Date: 2006
ISSN: 0271-2091
Statement of
J. W. Lee, M. D. Teubner, J. B. Nixon and P. M. Gill
Abstract: A three-dimensional, non-hydrostatic pressure, numerical model with k- equations for small amplitude free surface flows is presented. By decomposing the pressure 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 non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure-Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement.
Keywords: non-hydrostatic pressure
preconditioned GMRES
free surface flows
turbulence model
DOI: 10.1002/fld.1054
Published version:
Appears in Collections:Applied Mathematics publications
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