摘要:

AbstractIn this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that thedirectGalerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier‐Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requiresC1continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventionalC0elements. Numerical results using this approach for a wall‐driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two‐dimensional problem using thep‐version of the finite element method, the approach presented here is general and remains valid for the conventionalh‐version as well as three‐dimension

ISSN:0271-2091    

DOI:10.1002/fld.1650181102

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractFinite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δxmodes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity‐momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used.Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise‐free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the inte

ISSN:0271-2091    

DOI:10.1002/fld.1650181103

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractA numerical analysis is given for the application of streamwise diffusion to high‐intensity flows with marginal spatial resolution. Terms are added to the momentum equation which are similar to those used in the Petrov‐Galerkin, Taylor‐Galerkin and balancing tensor diffusivity methods. Values for the streamwise viscosity are obtained from mesh refinement studies. An illustration is given for the time‐dependent free convection of a liquid metal in a cavity with differentially heated sided walls. The spatial problem is solved with the Galerkin finite element method and the time integration is performed with the backward Euler method. Solution quality and computation time are compared for results with and without added streamwise diffusion. For the cases presented, streamwise diffusion eliminates spurious oscillations and saves computation time without compromising the s

ISSN:0271-2091    

DOI:10.1002/fld.1650181104

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractDissipative numerical approximations to the linear advection equation are considered with respect to their behaviour in the limit of weak dissipation. The context is wave propagation under typical far‐field conditions where grids are highly stretched and waves are underresolved. Three classes of schemes are analysed: explicit two‐level (i) symmetric and (ii) upwind schemes of optimal accuracy are considered as well as (iii) (symmetric) Runge‐Kutta schemes. In the far‐field the dissipation of all schemes diminishes. Group speeds of high‐frequency modes assume the incorrect sign and may admit ‘backward’ wave propagation if waves are not damped. A fundamental difference arises between the symmetric and upwind cases owing to the different rates at which the dissipation diminishes. In the upwind case, while the amount of damping per time step diminishes, the accumulative damping remains exponential in time. In the symmetric case the accumulative damping tends to unity, yielding in practice non‐dissipative schemes. In this light, parasitic modes constitute much less of a problem in the upwind case than in the symmetric case. Numerical tests confirm

ISSN:0271-2091    

DOI:10.1002/fld.1650181105

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractSolution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier‐Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods.For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector‐parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e.M×M×N, grids in three dimensions asNgets larger thanM. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector‐parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP‐8 and 9.2 Gflops on the NEC on SX3.For iterative methods, two approaches are developed. First, conjugate‐gradient‐like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side‐by‐side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rat

ISSN:0271-2091    

DOI:10.1002/fld.1650181106

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper presents a generalization of a computational method for the prediction of solute dispersion in fractured porous media. This method is specially useful for the prediction of subsurface flows in crystalline rocks. The model now includes a linear kinetics mechanism to represent the effects of sorption of radionuclides in the rock matrix. The method is improved in its accuracy and provides results useful for the assessment of radionuclide migration in high‐level, radioactive waste repositories. Results including verification (analytical) and physical test simulations are given. These results provide a partial validation of the numerical mode

ISSN:0271-2091    

DOI:10.1002/fld.1650181107

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn calculations of transonic flows it is necessary to limit the domain of computation to a size that is manageable by computers. At the boundary of the computational domain, boundary conditions are required to ensure a unique solution. Since wave solutions exist in the unsteady transonic flow field, incorrect boundary conditions may result in spurious reflections from the computational boundary. This may introduce errors into the solution. To prevent the spurious reflections, absorbing boundary conditions are often used on the computational boundary. In this paper we describe a method to derive absorbing boudary conditions for transonic calculations. We demonstrate both theoretically and numerically that the use of the absorbing boundary conditions will reduce the spurious reflections in the calculation.

ISSN:0271-2091    

DOI:10.1002/fld.1650181108

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650181109

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650181101

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY