Unsteady Convection Diffusion
A central issue in numerical solution of the Navier-Stokes equations is the fidelity
of a finite difference approximation scheme. Of course, one way of trying to improve
a scheme is to use high order methods. Thus Lax Wendroff schemes improve on
first order shemes and QUICKEST improves on Lax Wendroff.
I examined the use of an exact evolutionary operator for constant coefficient convection diffusion to systematically generate schemes of arbitrary order (see Morton & Sobey, 1991).
This work has been continued with Ercilia Sousa where we have looked at a range of
problems associated with convection diffusion equations, see
1998 Sousa, E. & Sobey, I.J. `Finite Difference Approximation of a Convection Diffusion Equation Near a Boundary' OU Computing Laboratory Report NA-98/16
2001 E. Sousa & I.J. Sobey 'A family of finite difference schemes for the convection-diffusion equation in two dimensions' OU Computing Laboratory Report NA-01/11
2002 E. Sousa & I.J. Sobey `A new perspective on the stability of unsteady stream-function vorticity calculations ' OU Computing Laboratory Report NA-02/03
2002 Sousa, E, & Sobey, I.J. 'On the influence of numerical boundary conditions'
Applied Numerical mathematics 41, p325-344
2002 Sousa, E, & Sobey, I.J. 'A family of finite difference schemes for the convection-diffusion equation in two dimensions' in Brezzi F,
Buffa A, Corsaro S, Murli F (Eds) -- Enumath 2001 Numerical Mathematics and Advanced Applications, Springer-Verlag, (2002) pp. 95-104.
2003 Sousa, E, & Sobey, I.J. 'Numerical stability of unsteady stream-function vorticity calculations' Communications in Numerical Methods in Engineering 19 pp407-419.
2004 E. Sousa & I.J. Sobey `Effect of boundary vorticity discretisation on explicit stream function - vorticity calculations' Departamento de Matematica, Universidade de Coimbra, Pre-Publicacoes, 04-17.
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