Abstract
Numerical experiments with discretization methods on nonuniform grids are presented for the convection-diffusion equation. These show that the accuracy of the discrete solution is not very well predicted by the local truncation error. The diagonal entries in the discrete coefficient matrix give a better clue: the convective term should not reduce the diagonal. Also, iterative solution of the discrete set of equations is discussed. The same criterion appears to be favourable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.J. Crowder and C. Dalton, Errors in the use of nonuniform mesh systems. J. Comput. Phys. 1 (1971) 32–45.
E. Kálnay de Rivas, On the use of nonuniform grids in finite difference equations. J. Comp. Phys. 10 (1972) 202–210.
E. Turkel, Accuracy of schemes with nonuniform meshes for compressible fluid flows. ICASE Report 85–43 (1985).
J. Pike, Grid adaptive algorithms for the solution of the Euler equations on irregular grids. J. Comp. Phys. 71 (1987) 194–223.
T.A. Manteuffel and A.B. White Jr., The numerical solution of second-order boundary value problems on nonuniform meshes. Math, of Comp. 47 (1986) 511–535.
A.E.P. Veldman, Who’s afraid of non-symmetric matrices? A discussion of elementary iterative methods. Report TWI 88-49, Delft University of Technology (1988).
D.M. Young, Iterative solution of large linear systems. New York: Academic Press (1971).
C. Rossow, Comparison of cell centered and cell vertex finite volume schemes. In: M. Deville (ed.), Proc. 7th GAMM Conf. on Numerical Fluid Dynamics. Braunschweig: Vieweg Verlag (1987) pp. 327–333.
M.G. Hall, Cell-vertex multigrid scheme for solution of the Euler equations. In: K.W. Morton and M.J. Baines (eds), Numerical Methods for Fluid Dynamics. Oxford: University Press (1986) pp. 303–345.
R.-H. Ni, A multiple grid scheme for solving the Euler equations. AIAA J. 20 (1982) 1565–1571.
A.E. Mynett, P. Wesseling, A. Segal and C.G.M. Kassels, The ISNaS incompressible Navier-Stokes solver: invariant discretization. Applied Scientific Research 48 (1991) 175–191.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Veldman, A.E.P., Rinzema, K. (1992). Playing with nonuniform grids. In: Kuiken, H.K., Rienstra, S.W. (eds) Problems in Applied, Industrial and Engineering Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2440-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-011-2440-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5076-0
Online ISBN: 978-94-011-2440-9
eBook Packages: Springer Book Archive