摘要:

AbstractThe work concerns cnoidal and solitary wave solutions of the Boussinesq equations in the context of finite difference methods. The existence of permanent wave‐forms is discussed and approximate solutions are found for one particular discrete formulation by perturbation techniques. These techniques can be applied to most difference and regular element discretizations of equations describing weakly non‐linear and dispersive waves. No proof of convergence of the perturbation expansions is established, but the appropriateness of the solutions is confirmed through comparison with the results of computer simulations. From the perturbation series it is found that the phase speed of solitons is useless for the evaluation of numerical methods and that asymmetries in the discrete equations may ruin the soliton solution. The availability of a discrete closed‐form solution is especially important for discussions concerning the existence and accuracy of permanent wave‐forms with oblique orientations relative to t

ISSN:0271-2091    

DOI:10.1002/fld.1650130602

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractWe present a new surface‐intrinsic linear form for the treatment of normal and tangential surface tension boundary conditions in C0‐geometry variational discretizations of viscous incompressible free‐surface flows in three space dimensions. The new approach is illustrated by a finite (spectral) element unsteady Navier‐Stokes analysis of the stability of a falling liqu

ISSN:0271-2091    

DOI:10.1002/fld.1650130603

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA boundary linear integral method based on Green function theory has been developed to solve the full potential equation for subsonic and transonic flows. In this integral method, potential values in the flow region are determined by potential values represented by boundary integrals and a volume integral. The boundary potential values are obtained by implementing the boundary integrals along boundary segments where a linear potential relation is assumed. The volume integral is evaluated in a grid generated by finite element discretization. The volume integral is evaluated only outside the body. Therefore there is no extra boundary treatment required for evaluation of the volume integral. The source term is assumed to be constant in an element integral volume. The volume integral needs to be evaluated only once and can be stored in computer memory for further usage.

ISSN:0271-2091    

DOI:10.1002/fld.1650130604

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAn efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two‐dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth‐order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall‐normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non‐similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high‐speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be igno

ISSN:0271-2091    

DOI:10.1002/fld.1650130605

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractHigh‐order compact finite difference schemes for two‐dimensional convection‐diffusion‐type differential equations with constant and variable convection coefficients are derived. The governing equations are employed to represent leading truncation terms, including cross‐derivatives, making the overallO(h4) schemes conform to a 3 × 3 stencil. We show that the two‐dimensional constant coefficient scheme collapses to the optimal scheme for the one‐dimensional case wherein the finite difference equation yields nodally exact results. The two‐dimensional schemes are tested against standard model problems, including a Navier‐Stokes application. Results show that the two schemes are generally more accurate, on comparable grids, thanO(h2) centred differencing and commonly usedO(h) andO(h3)

ISSN:0271-2091    

DOI:10.1002/fld.1650130606

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe Taylor‐least squares (TLS) scheme, developed to solve the unsteady advection‐diffusion equation for advection‐dominated cases in one and two dimensions, is extended to three dimensions and applied to some 3D examples to demonstrate its accuracy. The serendipity Hermite element is selected as an interpolation function on a linear hexagonal element. As a validation of the code and as a simple sensitivity analysis of the scheme on the different types of shape functions, the 2D example problem of the previous study is solved again. Four 3D problems, two with advection and two with advection‐diffusion, are also solved. The first two examples are advection of a steep 3D Gaussian hill in rotational flow fields. For the advection‐diffusion problems with fairly general flow fields and diffusion tensors, analytical solutions are obtained using the ray method. Despite the steepness of the initial conditions, very good agreement is observed between the analytical and TLS

ISSN:0271-2091    

DOI:10.1002/fld.1650130607

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAn upwind MUSCL‐type implicit scheme for the three‐dimensional Navier‐Stokes equations is presented and details on the implementation for three‐dimensional flows of a ‘diagonal’ upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson‐King non‐equilibrium model. Good predictions of separated two‐ and three‐dimensional flo

ISSN:0271-2091    

DOI:10.1002/fld.1650130608

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non‐linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non‐linearity and the coupling with the thermal boundary layer equation. Because the non‐linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solu

ISSN:0271-2091    

DOI:10.1002/fld.1650130609

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650130601

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY