摘要:

AbstractA new finite element method for solving the time‐dependent incompressible Navier‐Stokes equations with general boundary conditions is presented. The two second‐order partial differential equations for the vorticity and the stream function are factorized, apart from the non‐linear advection term, by eliminating the coupling due to the double specification on the stream function at (a part of) the boundary. This is achieved by reducing the no‐slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according to an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite difference equivalent by means of a few numerical examples. The results obtained using 4‐noded bilinear elements provide an illustration of the superiority of the finite element based spatial dis

ISSN:0271-2091    

DOI:10.1002/fld.1650040202

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe problem of fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite‐element method. The techniques of parameter‐stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width‐to‐height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The non‐linear branches above the critical Rayleigh number are examined. Extensions to non‐Boussinesq flow

ISSN:0271-2091    

DOI:10.1002/fld.1650040203

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe discontinuity of a finite‐element pressure field that is sometimes present in the neighbourhood of the pressure‐specification‐point is shown to arise either from round‐off, or from mistakes in modelling. The implications of this are considered. In particular it restricts grid refinement near the pressure‐specification‐point. The analysis can be extended to finite‐difference calculations, and to other fields governed by equations similar to Poiss

ISSN:0271-2091    

DOI:10.1002/fld.1650040204

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe boundary integral equation method is a numerical technique extensively applied in the solution of boundary value problems from many different engineering fields. The starting point of the method is the formulation of an integral equation which gives the variable at any point in terms of single and double layer potentials whose densities are the values of the variable and its derivatives on the boundary. The method consists of the numerical solution of this integral equation when the field point is taken to lie on the boundary. The present paper extends the formulation of the method to Stokes flows of a collection of particles in infinite circular cylinders. This is achieved by developing matrix Green's functions for Stokes flows in cylindrical boundaries. The results are found to be in good agreement with the results of Wang and Skalak1and Tözeren.

ISSN:0271-2091    

DOI:10.1002/fld.1650040205

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractRecent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power‐law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary‐layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary‐integral formulation replaces the finite‐element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco‐elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite‐element treatment (in time‐dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first‐normal‐stress difference to shear stress turns out to be generallyO(10).) The predictions also correlate very well with experimental biref

ISSN:0271-2091    

DOI:10.1002/fld.1650040206

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractAn approach for the numerical solution of flow problems based on the concept of fundamental solutions of differential equations is described. This approach uses the finite element methodology but does not rely on the concept of variational principle or that of residuals. The approach is shown to be well‐suited for many types of flow problems. Various applications of this approach are discussed in this paper, with particular emphasis placed on the solution of potential flows and viscous flows containing appreciable regions of separatio

ISSN:0271-2091    

DOI:10.1002/fld.1650040207

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650040208

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650040209

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650040201

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY