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A novel finite difference formulation for differential expressions involving both first and second derivatives

โœ Scribed by D. B. Spalding

Publisher
John Wiley and Sons
Year
1972
Tongue
English
Weight
395 KB
Volume
4
Category
Article
ISSN
0029-5981

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โœฆ Synopsis

I t is shown that the upwind difference scheme of formulating differential expressions, in problems involving transport by simultaneous convection and diffusion, is superior to the central difference scheme, when the local Peclet number of the grid is large. Even better schemes are derived and discussed. It is pointed out that the best finite difference analogues are found by approximating differential expressions as a whole, and that simple (e.g. one-dimensional) exact solutions form a useful, legitimate and independent source of these optimum algebraic formulae.

๐Ÿ“œ SIMILAR VOLUMES

Finite element methods for second order
Finite element methods for second order differential equations with significant first derivatives
โœ I. Christie; D. F. Griffiths; A. R. Mitchell; O. C. Zienkiewicz ๐Ÿ“‚ Article ๐Ÿ“… 1976 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 316 KB

## Abstract Galerkin finite element methods based on symmetric pyramid basis functions give poor accuracy when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is such that oscillations are present in the numeric