摘要:

AbstractIn this paper we describe finite element computations of the free‐surface flow of a viscous fluid down an undulating inclined plane. The technique developed here employs an orthogonal mapping that is computed along with the velocity and pressure. This is allied to a technique to compute symbolically the Jacobian and other derivatives required for numerical continuation methods. The solutions obtained are compared with laboratory experiments and finite element computations reported by Pritchard and co‐workers. The finite element computational method used by these authors employs spines to represent the free surface. An excellent agreement is shown to exist between the new computations and the laboratory experiments, and with the numerical solutions of Pritchard and co‐wo

ISSN:0271-2091    

DOI:10.1002/fld.1650151102

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA flux‐based modified method of characteristics (MMOC) methodology in 1D is described which has the following properties: unconditional stability (though explicit), exact answers for integerCFL(Courant) numbers, completely conservative (locally and globally) and able to utilize various flux limiters and various characteristic‐ (trajectory‐) tracking algorithms. The use of characteristics based on cell‐wise constant characteristic velocities results in considerable code simplification, and Van Leer's MUSCL is an accurate and cost‐effective flux limiter. ForCFL≥1 the flux limiter is applied only to the non‐integer part ofCFL, whereas the integer part is exact for constant velocities; therefore accuracy improves with largerCFL. It is not a cheap algorithm, although explicit, because the operation count per time step increases with the integer part ofCFL, but it is much more accurate than the commonly used implicit upstream differencing. This flux‐based MMOC method is well suited for groundwater flow calculations in which large local Courant numbers arise owing to

ISSN:0271-2091    

DOI:10.1002/fld.1650151103

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis work describes a practical way of constructing a spectral representation of linear boundary value problems (BVPs) using a tau method. All BVPs are treated as first‐order systems, unlike most implementations which tend to view the problem in terms of a single high‐order differential equation. For most applications this formulation will adhere more closely to the natural derivation of the original equations from, for example, a series of conservation laws. The technique is exemplified for Chebyshev polynomials in a variety of real applications, although detailed results are provided for any polynomial ba

ISSN:0271-2091    

DOI:10.1002/fld.1650151104

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Two flow problems are considered: (i) three‐dimensional flow near a stagnation point and (ii) axisymmetric flow due to stretching of a sheet. Both flows are characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. The exact numerical solutions are obtained using the technique described in the paper. Also, the first‐order perturbation solutions (in terms of the viscoelastic fluid parameter) are derived. A comparison of the results shows that the perturbation method is inadequate in predicting some of the vital characteristic features of the flows, which can possibly be revealed only by the exact numerical solut

ISSN:0271-2091    

DOI:10.1002/fld.1650151105

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA fourth‐order method, without using extrapolation, is developed for the steady‐state solution of a non‐linear system of three simultaneous partial differential equations for the flow of a fluid in a heated closed cavity. The method is a finite difference method which has converged for all Rayleigh numbersRaof physical interest and all Prandtl numbersPrattempted. The results are presented and compared with some of the accurate results available in de Vahl Davis and Jones, Shay and Schultz, and Dennis and Hudson. The method used to develop the fourth‐order method presented in this paper can be used to develop high‐order methods for other partial differential equations. The method was developed to be stable without using the upwinding

ISSN:0271-2091    

DOI:10.1002/fld.1650151106

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid‐dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier‐Stokes (NS) equations are approximated with a reduced Navier‐Stokes (RNS) system, that represents the lowest‐order terms in an asymptoticReexpansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher‐order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co‐ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward‐facing

ISSN:0271-2091    

DOI:10.1002/fld.1650151107

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650151108

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650151109

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650151101

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY