摘要:

AbstractIn this study, the discretized finite volume form of the two‐dimensional, incompressible Navier‐Stokes equations is solved using both a frozen coefficient and a full Newton non‐linear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate‐gradient‐like method (CGSTAB). Various types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test

ISSN:0271-2091    

DOI:10.1002/fld.1650180302

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper a new, highly accurate method called PH is presented for the numerical integration of partial differential equations. The method is applied for the solution of the one‐dimensional diffusion equation. Upon integrating the equation within a subdomain of space and time using the prismoidal approximation, a three‐point implicit scheme is obtained with a truncation error of orderO(k4,h6), wherekandhrepresent the time and space steps respectively. The method is stable under the conditions= αk/h2⩽S(δ), where the functionS(δ) increases as the parameter δ decreases from 1/12 to negative values. In practice the method behaves as unconditionally stable upon choosing an appropriate value for δ. A new formula is also adopted for the implementation of a Neumann boundary condition, introducing a truncation error of orderO(h4). Numerical solutions are obtained incorporating Dirichlet and Neumann boundary conditions. The results prove that our method is far more accurate than any other‐implicit or exp

ISSN:0271-2091    

DOI:10.1002/fld.1650180303

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractSemi‐Lagrangian methods are now perhaps the most widely researched algorithms in connection with atmospheric flow simulation codes. In order to investigate their applicability to hydraulic problems, cubic Hermite polynomials are used as the interpolant technique. The main advantage of such an approach is the use of information from only two points. The derivatives are calculated and limited so as to produce a shape‐preserving solution. The lack of conservation of semi‐Lagrangian methods, however, is widely regarded as a serious disadvantage for hydraulic studies, where non‐linear problems in which shocks may develop are often encountered. In this work we describe how to make the scheme conservative using an FCT approach. The method proposed does not guarantee an unconditional shock‐capturing ability but is able to correctly reproduce the discontinuous flows common in open channel simulation without any shock‐fitting algorithm. It is a cheap way to improve existing 1D semi‐Lagrangian codes and allows stable calculations beyond the usual CFL limits. A basic semi‐Lagrangian method is presented that provides excellent results for a linear problem: the new techniques allow us to tackle non‐linear cases without unduly degrading the accuracy for the simpler problems. Two one‐dimensional hydraulic problems are used as test cases, water hammer and dam break. In the latter case, because of the non‐linearity, special care is needed with the low‐order solution and we show the advantages of using Leveque's large‐time step version of Roe'

ISSN:0271-2091    

DOI:10.1002/fld.1650180304

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIt is shown that the eddy viscosity profile in a quasi‐three‐dimensional numerical tidal and storm surge model can be estimated by assimilation of velocity data from one or more current meters located on the same vertical line. The computational model used is a simplified version of the so‐called vertical/horizontal splitting algorithm proposed by Lardner and Cekirge. We have estimated eddy viscosity both as a constant and as a variable parameter. The numerical scheme consists of a two‐level leapfrog method to solve the depth‐averaged equations and a generalized Crank‐Nicolson scheme to compute the vertical profile of the velocity field. The cost functional in the adjoint scheme consists of two terms. The first term is a certain norm of the difference between computed and observed velocity data and the second term measures the total variation in the eddy viscosity function. The latter term is not needed when the data are exact for the model but is necessary to smooth out the instabilities associated with ‘noisy’ data. It is shown that a satisfactory minimization can be accomplished using either the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) quasi‐Newton algorithm or Nash's truncated Newton algorithm. Very effective estimation of eddy viscosity profiles is shown to be achieved even when the amount

ISSN:0271-2091    

DOI:10.1002/fld.1650180305

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractA three‐dimensional extension of the QUICK scheme adapted for the finite volume method and non‐uniform grids is presented to handle convection‐diffusion problems for high Peclet numbers and steep gradients. The algorithm is based on three‐dimensional quadratic interpolation functions in which the transverse curvature terms are maintained and the diagonal dominance of the coefficient matrix is preserved. All formulae are explicitly given in an appendix. Results obtained with the classical upwind (UDS), the simplified QUICK (transverse terms neglected) and the present full QUICK schemes are given for two benchmark problems, one two‐dimensional, steady state and the other three‐dimensional, unsteady state. Both QUICK schemes are shown to give superior solutions compared with the UDS in terms of accuracy and efficiency. The full QUICK scheme performs better than the simplified QUICK, giving even for coarse grids acceptable results closer to the analytical solutions, while the computational time is not af

ISSN:0271-2091    

DOI:10.1002/fld.1650180306

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650180307

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650180301

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY