An improved (9,5) higher order compact scheme for the transient two-dimensional convection-diffusion equation

In the present study, we propose an implicit, unconditionally stable high order compact (HOC) finite difference scheme for the unsteady two‐dimensional (2‐D) convection–diffusion equations. The scheme is second‐order accurate in time and fourth‐order accurate in space. The stencil requires nine poin...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2006-07, Vol.51 (7), p.703-717
Main Authors: Kalita, Jiten C., Chhabra, Puneet
Format: Article
Language:English
Subjects:
2-D
accuracy
Computational methods in fluid dynamics
convection-diffusion
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
HOC
N-S equations
Physics
unsteady
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Summary:In the present study, we propose an implicit, unconditionally stable high order compact (HOC) finite difference scheme for the unsteady two‐dimensional (2‐D) convection–diffusion equations. The scheme is second‐order accurate in time and fourth‐order accurate in space. The stencil requires nine points at the nth and five points at the (n+ 1)th time level and is therefore termed a (9,5) HOC scheme. It efficiently captures both transient and steady solutions of linear and nonlinear convection–diffusion equations with Dirichlet as well as Neumann boundary conditions. It is applied to a linear Gaussian pulse problem, a linear 2‐D Schrödinger equation and the lid driven square cavity flow governed by the 2‐D incompressible Navier–Stokes (N–S) equations. The results are presented and are compared with established numerical results. Excellent comparison is obtained in all the cases. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.1133