摘要:

AbstractA finite element CFD algorithm is developed for Euler and Navier‐Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second‐order‐accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion‐error control mechanisms; (2) a stiffly stable second‐order‐accurate implicit Rosenbrock‐Runge‐Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large‐matrix statement. Thorough analyses are presented regarding well‐posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi‐one‐ and two‐dimensional Euler and Navier‐Stokes benchmark test problems. Of critical importance, essentially non‐oscillatory solutions are uniformly attained for a range of supercritica

ISSN:0271-2091    

DOI:10.1002/fld.1650120502

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractEigensystem analysis techniques are applied to finite difference formulations of the Navier‐Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix.On the basis of the pattern of eigenvalue distributions for various flow configurations, ashiftingof the implicit operators in question is devised. The idea of shifting is based on the power method of linear algebra and is very simple to implement. This procedure has improved the rates of convergence of CFD codes (developed at NASA Ames Research Center) by 20%–50%. The sensitivity of the computed solution with respect to theshiftis also studied. Finally, an adaptive shifting of the spectrum together with Wynn's acceleration algorithm are discussed. It turns out that the shifting process is a preconditioner for Wynn's met

ISSN:0271-2091    

DOI:10.1002/fld.1650120503

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe unsteady incompressible Navier‐Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50–200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi‐steady state. A new integral‐series method is developed for the far‐field streamfunction condition on a finite two‐dimensional computational domain. The use of fourth‐order Hermitian relations for the convection terms in the conservation‐form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex‐shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behaviour of the shedding frequency are presented

ISSN:0271-2091    

DOI:10.1002/fld.1650120504

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA smoothing technique is applied to improve the stability of a semi‐implicit time integrator for the three‐dimensional shallow water equations. In this method the terms involving the vertical direction are treated implicitly. The stability condition on the time step depends only on the horizontal mesh sizes; therefore in the horizontal‐direction a smoothing operator is added. Owing to the smoothing, the maximally stable time step increases considerably while the accuracy is hardly affected. Moreover, it turns out that the smoothing operator is efficient on vector and parallel comp

ISSN:0271-2091    

DOI:10.1002/fld.1650120505

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA discretization scheme is presented which, unlike the standard higher‐order finite difference and spline methods, does not give rise to unphysical solution modes and boundary conditions. Practical application of this scheme is achieved via the DCMG algorithm recently developed by the same author, which turns out to be able to find a converged solution of the ψ‐ζ Navier‐Stokes equations in about the same time for highorder as for low‐order discretization schemes. Examples are presented for the driven cavity problem to explore the accuracy of the new method. Finally, a local analysis is performed of the corner singularities which exist in driven cavity flow, and their effect on the overall accuracy of the solutions obtained by polynomial interpolation methods is inv

ISSN:0271-2091    

DOI:10.1002/fld.1650120506

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650120501

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY