摘要:

AbstractFinite element solution methods for the incompressible Navier‐Stokes equations in primitive variables form are presented. To provide the necessary coupling and enhance stability, a dissipation in the form of a pressure Laplacian is introduced into the continuity equation. The recasting of the problem in terms of pressure and an auxiliary velocity demonstrates how the error introduced by the pressure dissipation can be totally eliminated while retaining its stabilizing properties. The method can also be formally interpreted as a Helmholtz decomposition of the velocity vector.The governing equations are discretized by a Galerkin weighted residual method and, because of the modification to the continuity equation, equal interpolations for all the unknowns are permitted. Newton linearization is used and at each iteration the linear algebraic system is solved by a direct solver. Convergence of the algorithm is shown to be very rapid. Results are presented for two‐dimensional flows in various geometr

ISSN:0271-2091    

DOI:10.1002/fld.1650130202

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAn adaptive strategy for the finite element solution of three‐dimensional viscous flow problems is defined and implemented. The solution strategy is based on an advancing front mesh generator making use of binary data structures for fast geometrical data handling. The error is estimated aposterioriwith a residual‐type bound. The error estimate is shown to exhibit proper convergence for tetrahedral elements. Its combination with the mesh generator and an interpolation scheme for unstructured meshes is shown to generate adaptive meshes and to reduce the solution cost for a given error level, as illustrated by the isothermal flow of a shear‐thinning

ISSN:0271-2091    

DOI:10.1002/fld.1650130203

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThis paper is concerned with a number of upstream‐weighted second‐ and third‐order difference schemes. Also considered are the conventional upwind and central difference schemes for comparison. It commences with a general difference equation which unifies all the given first‐, second‐ and third‐order schemes. The various schemes are evaluated through the use of the general equation. The unboundedness and accuracy of the solutions by the difference schemes are assessed via various analyses: examination of the coefficients of the difference equation, Taylor series truncation error analysis, study of the upstream connection to numerical diffusion, single‐cell analysis. Finally, the difference schemes are tested on one‐ and two‐dimensional model problems. It is shown that the high‐order schemes suffer less from the problem of numerical diffusion than the first‐order upwind difference scheme. However, unboundedness cannot be avoided in the solutions by these schemes. Among them the linear upwind difference scheme presents the best compromise between numerical diffusion and s

ISSN:0271-2091    

DOI:10.1002/fld.1650130204

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThis study identifies the key parameters upon which energy absorption at artificial boundaries depends. A thorough numerical study is presented, of typical reflections from open computational boundaries, for problems governed by hyperbolic systems of equations. The emphasis is on systems, where it is often the combination of all boundary procedures that determine the quality of boundary treatment. We study dissipative numerical models which have so far not been analysed to the same extent as non‐dissipative models and employ a Law‐Wendroff‐type scheme as a prototype. While it is widely accepted that dissipative models tend to give fewer problems than non‐dissipative ones, we show a variety of cases where substantial reflections do occur even in ID and quasi‐ID set‐ups, where theory predicts best results. This can partly be explained by the vanishing of dissipation in the far field. Group velocity analysis, justifiable on the grounds of weak dissipation, predicts a pathological behaviour which is confirmed by numerical experiments. We demonstrate strong focusing of asymptotic errors generated at the artificial boundary. Internal reflections due to slowly expanding grids are shown for non‐linear systems. The need for high‐frequency boundary conditions naturally arises and combined low‐high‐frequency boundary recipes following Higdon, Vichnevetsky and Pariser are adapted to systems and tested. Partial cures are also discussed, mainly in terms of pointing out their theoreticall

ISSN:0271-2091    

DOI:10.1002/fld.1650130205

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA three‐dimensional spectral algorithm for the solution of Stokes flow between eccentrically rotating cylinders is described. Included in the model are pressure boundary conditions at the two ends of the finite length cylinders and the effect of a fluid line source on the inner cylinder. A comparison of results for the load and couple on the inner cylinder is made with those available from lubrication theory in the absence of a line source. Good agreement is shown for long, short and finite journal bearings when the various geometrical assumptions inherent in the lubrication analysis are satisfie

ISSN:0271-2091    

DOI:10.1002/fld.1650130206

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA method is presented for solving the 3D hydrodynamic equations in homogeneous sea regions using the Galerkin approach in the vertical with a mixed basis set. The basis set is composed of eigenfunctions of the eddy viscosity profile and a fixed function through the vertical, the amplitude of which is related to the externally applied surface wind stress. By this means the high‐shear near‐surface layer, which has previously been difficult to resolve using eigenfunction expansions, is accurately represented in the solution.The computational advantages of this approach compared with other basis functions, in terms of computer time and memory, and the ease of implementation on parallel processors with vector facilities are briefly discussed.The accuracy of the method and the choice of the additional function is demonstrated for the problem of wind‐induced currents in a rectangular sea region.Calculations clearly show that for wind‐induced currents this new approach is significantly more accurate than the ‘classical’ eigenfunction method. Also, the new method retains the advantages of the eigenfunction approach, namely insight into the mechanisms involved and ease of implementation on vector‐parallel computers, together with minimization of computer ti

ISSN:0271-2091    

DOI:10.1002/fld.1650130207

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe PROSPER General Circulation Model (PGCM) is a three‐dimensional model based on the incompressible Navier‐Stokes equations, an equation of state and the heat equation. The hydrostatic approximation and the rigid lid approximation are used. The system of equations is converted into an equivalent form in which the surface pressure is more directly expressed in terms of a two‐dimensional Poisson equation. The finite difference method is described and analysed. In particular, the iteration method within every time step to determine the new surface pressure and velocity components, and numerical diffusion aspects due to the use of the staggered Arakawa‐C grid are looked at. Since part of the development of the PGCM code is a result of studying the Sandia Ocean Modelling System (SOMS), a comparison is made with respect to the concepts used in both

ISSN:0271-2091    

DOI:10.1002/fld.1650130208

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650130209

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650130201

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY