摘要:

AbstractMany fluid flow problems of current interest occur in domains that are mappable to a rectangle or a box; conformal mappings are particularly useful in this regard. We are concerned here with the efficient solution of such problems using finite elements. The central issue is the element choice, and this issue is addressed in terms of operation counts, computer memory and I/0 requirements, and the extent to which code vectorization is possible. It is concluded that rectangular (box) elements generally lead to more efficient algorithms that triangular (tetrahedral) elements. A synthesis of algorithms, based on bilinear (trilinear) elements, is presented. The algorithms have the attributes of simplicity, accuracy, stability and straightforward incorporation of boundary conditions. For bilinear and trilinear elements, it is found that product and first‐derivative terms are well‐handled by the Galerkin FE method, but that it is advantageous to go outside of the Galerkin framework when treating second‐derivative terms. It is particularly important to consider the form of the governing equations,vis‐à‐visthe choice of staggered, non‐staggered and/or mixed‐order elements, and to choose an appropriate time scheme. The described techniques have been successfully applied to a variety of problems in regular domains, including the solution of the three‐dimensional time‐dependent hydrostatic primitive equations; these are stiff and include first and second derivative terms, non‐linearities and variable coefficients due to

ISSN:0271-2091    

DOI:10.1002/fld.1650070102

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThe incompressible, two‐dimensional Navier‐Stokes equations are solved by the finite element method (FEM) using a novel stream function/vorticity formulation. The no‐slip solid walls boundary condition is applied by taking advantage of the simple implementation of natural boundary conditions in the FEM, eliminating the need for an iterative evaluation of wall vorticity formulae. In addition, with the proper choice of elements, a stable scheme is constructed allowing convergence to be achieved for all Reynolds numbers, from creeping to inviscid flow, without the traditional need for upwinding and its associated false diffusion. Solutions are presented for a variety of geome

ISSN:0271-2091    

DOI:10.1002/fld.1650070103

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractWe study the generation of periodic velocity and temperature fields in a plane horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals, although the present paper is limited to two‐dimensional flows. We use transient finite difference and finite element algorithms which lead to identical results. We demonstrate the oscillatory mechanism in two different geometrie

ISSN:0271-2091    

DOI:10.1002/fld.1650070104

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractWe study the steady‐state three‐dimensional flow which occurs in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals. We find that three‐dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two‐dimensional counterpart. We also investigate the sensitivity of the flow to non‐symmetric dis

ISSN:0271-2091    

DOI:10.1002/fld.1650070105

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractIn general Stokes problems, no boundary conditions exist for the pressure. But pressure is anL2(Ω) function and can uniquely be represented as the divergence of a precisely defined vector field. In the 2‐D case, this vector field can in turn be represented as the sum of a gradient (of a pressure‐potential) and the curl of a second scalar potential. The latter potential is entirely determined by the first one. A variational equation is obtained for such pressure potential class, which exists and is uniquely characterized. This variational problem is well‐posed. Finite element approximations can easily be realized and ensure high convergence rates for theL2(Ω) norm of the p

ISSN:0271-2091    

DOI:10.1002/fld.1650070106

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650070107

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650070101

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY