摘要:

AbstractComputational difficulties arise in the non‐linear free‐surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite‐amplitude programs. When Southwell and Vaisey1first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long

ISSN:0271-2091    

DOI:10.1002/fld.1650050602

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA solution adaptive grid (SAG) method which redistributes the nodal points of a function according to its curvature is presented. A single, user‐selected step parameter,P, is available for controlling the maximum step size, allowing the application of the technique to a wide variety of problems. Three test cases are cited: (1) the 1‐dimensional inviscid Burgers equation, (2) the Falkner‐Skan equation and (3) the finite‐volume form of the Navier‐Stokes equations for transonic aerofoil flows. In all three cases, significant solution improvement in terms of accuracy and convergence acceleration were

ISSN:0271-2091    

DOI:10.1002/fld.1650050603

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractExact periodic solutions are generated for the 3‐D hydrodynamic equations in linearized form. A linear slip condition is enforced at the bottom, based on the velocity at the bottom. It is shown that the bottom stress can be equivalently expressed in terms of the vertically averaged velocity, and expressions for this bottom stress coefficient are derived in terms of the primary parameters of the problem. As a result, the three‐dimensional structure may be assembled from conventional solutions to (a) the 1‐D vertical diffusion equation; and (b) the 2‐D vertically averaged shallow water equations. In the latter, the bottom stress effects are shown to be complex and frequency‐dependent, and an additional rotational term is required for their repre

ISSN:0271-2091    

DOI:10.1002/fld.1650050604

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA numerical procedure was developed to solve the two‐dimensional and axisymmetric incompressible laminar boundary layer equations using the semi‐discrete Galerkin finite element method. Linear Lagrangian, quadratic Lagrangian, and cubic Hermite interpolating polynomials were used for the finite element discretization; the first‐order, the second‐order backward difference approximation, and the Crank‐Nicolson method were used for the system of non‐linear ordinary differential equations; the Picard iteration and the Newton‐Raphson technique were used to solve the resulting non‐linear algebraic system of equations. Conservation of mass is treated as a constraint condition in the procedure; hence, it is integrated numerically along the solution line while marching along the time‐like co‐ordinate. Among the numerical schemes tested, the Picard iteration technique used with the quadratic Lagrangian polynomials and the second‐order backward difference approximation case turned out to be the most efficient to achieve the same accuracy. The advantages of the method developed lie in its coarse grid accuracy, global computational efficiency, and wide applicability to most situations that may arise in incompressible laminar

ISSN:0271-2091    

DOI:10.1002/fld.1650050605

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractPrevious three‐dimensional simulations of the lid‐driven cavity flow have reproduced only the most general features of the flow. Improvements to a finite difference code, REBUFFS, have made possible the first completely successful simulation of the three‐dimensional lid‐driven cavity flow. The principal improvement to the code was the incorporation of a modified QUICK scheme, a higher‐order upwind finite difference formulation. Results for a cavity flow at a Reynolds number of 3200 have reproduced experimentally observed Taylor‐Görtler‐like vortices and other three‐dimensional effects heretofore not simulated. Experimental results obtained from a unique experimental cavity facility validate the ca

ISSN:0271-2091    

DOI:10.1002/fld.1650050606

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractPresented in this paper is a new method for the prediction of unsteady, incompressible separated flow over a two‐dimensional aerofoil. The algorithm was developed from an existing unsteady potential flow model1and makes use of an inviscid formulation for the flow field. The aerofoil is represented by vortex panels of linearly varying strength which are piecewise continuous at the corners. Discrete vortices with finite cores are used to model the separating shear layers.Following a brief summary of unsteady separation modelling, the theoretical framework is presented and the subsequent numerical implementation is discussed in detail.Results are given for flows which tend asymptotically to the steady state and conclusions are drawn regarding the usefulness of the metho

ISSN:0271-2091    

DOI:10.1002/fld.1650050607

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractIn this note we show that the numerical solution of the advection‐diffusion equation can be improved by considering the asymptotic behaviour of its analytical solution. This is accomplished by including a correction term based on the numerical differentiation of the asymptotic (Pe» 1,Pebeing the Peclet number) solution. This correction forces the usual oscillations associated with centred schemes to disappe

ISSN:0271-2091    

DOI:10.1002/fld.1650050608

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650050609

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650050610

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650050601

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY