摘要:

AbstractIt is commonly, but erroneously, assumed that the best way to treat upwind (closed) boundaries in numerical approximations of hyperbolic equations consists in a literal transcription, letting the numerical value be equal to the prescribed value. This results in a total reflection of spurious solutions that may arrive at the boundary from the computing domain. Those reflected solutions cannot be distinguished from consistent solutions, and they may seriously degrade the overall accuracy. We show that modifications of this treatment of the boundary may result in the absorption of spurious solutions. The effect of the absorbing properties of these boundary schemes is analyzed in Fourier space. We also analyze their numerical stability properties, and their effect on the accuracy of solutions generated in response to a time dependent boundary condition.

ISSN:0749-159X    

DOI:10.1002/num.1690020102

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

摘要:

AbstractPenalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth‐order problems in whichC1‐continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce theC1‐continuity constraint appears promising. In this study we demonstrate equivalence of the finite‐element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is

ISSN:0749-159X    

DOI:10.1002/num.1690020103

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

摘要:

AbstractA family of methods is developed for the numerical solution of second‐order parabolic partial differential equations in one space dimension. The methods are second‐, third‐, or fourth‐order accurate in time; five of them are seen to beL0‐stable in the sense of Gourlay and Morris, while the sixth is seen to beA0‐stable, The methods are tested on four problems from the literature, three diffusion problems and one reaction–diff

ISSN:0749-159X    

DOI:10.1002/num.1690020104

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

摘要:

AbstractThe two‐dimensional flow of an internally heated fluid in a circular vessel has been investigated by using a finite‐control‐volume numerical model. It has been found that, when symmetry constraints are imposed along the vertical midplane of the vessel, two distinct flow patterns can he predicted for the same operating conditions, a jet‐momentum‐dominated pattern and buoyancy‐dominated pattern. These patterns occur in an operating region where momentum and buoyancy forces are of comparable magnitude. However, when the symmetry constraints are removed and the full vessel cross section is modeled, only the buoyancy‐dominated pattern is observed. Results for the two cases are described and possible reasons for the differences in behavior

ISSN:0749-159X    

DOI:10.1002/num.1690020105

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

摘要:

AbstractOne‐step integration methods of fourth‐order accuracy using an odd number of function evaluationsK, to solvedy/dt= A ·y, are proposed. These methods have an imaginary stability limit\documentclass{article}\pagestyle{empty}\begin{document}$ S_{1\;} = \sqrt {(K - 1)^2 - 4} $\end{document}. In the caseK= 5 the Kutta‐Merson method r

ISSN:0749-159X    

DOI:10.1002/num.1690020106

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

摘要:

AbstractRecently, variational methods have been used to numerically generate grids on geometometric objects such as plane regions, volumes, and surfaces. This article presents a new method of determining variational problems that can be used to control such properties of the grid as the spacing of the points, area or volume of the cells, and the angles between the grid lines. The methods are applied to curves, surfaces, and volumes in three‐dimensional space; then segments, plane curves, and plane regions appear as special cases of the general discussion. The methods used here are simpler and clearer and provide more direct control over the grid than methods that appear elsewhere. The methods are applicable to any simply connected region or any region that can be made simply connected by inserting artificial boundaries. The methods also generalize easily to solution‐adaptive methods.An important ingredient in our method is the notion of a reference grid. A reference grid is defined on a region that is simpler, but analogous to, the geometric object on which a grid is desired. Variational methods are then used to transfer the reference grid to the geometric object. This gives simple and precise control of the local properties of the g

ISSN:0749-159X    

DOI:10.1002/num.1690020107

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690020101

出版商:John Wiley&Sons, Inc.    

年代:1986

数据来源: WILEY