摘要:

AbstractA time‐implicit numerical method for solving unsteady incompressible viscous flow problems is introduced. The method is based on introducing intermediate compressibility into a projection scheme to obtain a Helmholtz equation for a pressure‐type variable. The intermediate compressibility increases the diagonal dominance of the discretized pressure equation so that the Helmholtz pressure equation is relatively easy to solve numerically. The Helmholtz pressure equation provides an iterative method for satisfying the continuity equation for time‐implicit Navier–Stokes algorithms. An iterative scheme is used to simultaneously satisfy, within a given tolerance, the velocity divergence‐free condition and momentum equations at each time step. Collocated primitive variables on a non‐staggered finite difference mesh are used. The method is applied to an unsteady Taylor problem and unsteady laminar flow past a circul

ISSN:0271-2091    

DOI:10.1002/fld.1650140102

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA method to determine three‐dimensional die shapes from extrudate swell and vice versa is presented using a three‐dimensional Galerkin finite element method based on a streamlined formulation with the fluid velocities and pressures represented by triquadratic and trilinear basis functions respectively. The three‐dimensional streamlined method, an extension of the two‐dimensional formulation, uses successive streamsurfaces to form a boundary‐conforming co‐ordinate system. This produces a fixd, computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u,v,w,p). The extrudate produced by a die of a given shape is considered for moderate Reynolds numbers. Finally, the method is extended to address the problem of die design, where a die profile is sought to produce a target extr

ISSN:0271-2091    

DOI:10.1002/fld.1650140103

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA straightforward moving grid finite element method is developed to solve the one‐dimensional coupled system of non‐linear partial differential equations (PDEs) governing two‐ and three‐phase flow in porous media. The method combines features from a number of self‐adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle‐free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non‐linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single‐front two‐phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two‐ and three‐phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is al

ISSN:0271-2091    

DOI:10.1002/fld.1650140104

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non‐linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single‐ and double‐front simulations for two‐ and three‐phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non‐linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non‐zero value for the repulslive force to avoid development of an ill‐conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstanc

ISSN:0271-2091    

DOI:10.1002/fld.1650140105

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper is concerned with iterative techniques for the solution of the linear system of equations arising from a finite element approximation of an elliptic partial differential equation by a mixed method. Three types of iterative algorithms are investigated. Applications to the Stokes equations are discussed and the results of numerical experiments given.

ISSN:0271-2091    

DOI:10.1002/fld.1650140106

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper is devoted to the finite element analysis of heat transfer during melting in rectangular enclosures. The effects of aspect ratio and subcooling on the motion of the interface and the Nusselt number have been investigated. The different schemes employed in the present work throw useful light on the choice of the appropriate method for dealing with such phase change problems.

ISSN:0271-2091    

DOI:10.1002/fld.1650140107

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA parallel algorithm for the solution of potential flow problems using the panel method of Hess and Smith and conjugate and bi‐conjugate gradient techniques is presented. Analysis of the parallelism for the matrix. solvers shows the algorithms to have scalable properties as the problem size grows indefinitely large. Speed‐up and efficiency values are presented along with experimental and theoretical values for the optimum number of processors for maximum speed‐up. It is envisaged that the parallel techniques presented here have applications using other boundary integral methods for solving engineering problems of a more complex n

ISSN:0271-2091    

DOI:10.1002/fld.1650140108

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThree‐dimensional algorithms for the numerical computation of flows caused by tides or meteorological forcing are developed for four of Arakawa's spatial grid types using a spectral method in the vertical dimension. Three of the grids, in which the velocity components are computed at the same grid points, offer potential advantages over the commonly used C‐grid. The computed results from the four grids are compared for three test problems based on the linearized hydrodynamical equations. It is concluded that the B‐grid provides a viable alternative to the C‐grid, with significant advantages when a spectral method

ISSN:0271-2091    

DOI:10.1002/fld.1650140109

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650140110

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650140101

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY