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An improved (9,5) higher order compact scheme for the transient two‐dimensional convection–diffusion equation
Author(s) -
Kalita Jiten C.,
Chhabra Puneet
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1133
Subject(s) - stencil , mathematics , mathematical analysis , convection–diffusion equation , neumann boundary condition , nonlinear system , compact finite difference , dirichlet boundary condition , compressibility , navier–stokes equations , boundary value problem , finite difference method , physics , mechanics , computational science , quantum mechanics
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 n th 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.