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A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. (English) Zbl 1094.76546
Summary: A class of higher order compact (HOC) schemes has been developed with weighted time discretization for the two-dimensional unsteady convection-diffusion equation with variable convection coefficients. The schemes are second or lower order accurate in time depending on the choice of the weighted average parameter $\mu$ and fourth order accurate in space. For $0·5\le \mu \le 1$, the schemes are unconditionally stable. Unlike usual HOC schemes, these schemes are capable of using a grid aspect ratio other than unity. They efficiently capture both transient and steady solutions of linear and nonlinear convection-diffusion equations with Dirichlet as well as Neumann boundary condition. They are applied to one linear convection-diffusion problem and three flows of varying complexities governed by the two-dimensional incompressible Navier-Stokes equations. Results obtained are in excellent agreement with analytical and established numerical results. Overall the schemes are found to be robust, efficient and accurate.
##### MSC:
 76M20 Finite difference methods (fluid mechanics) 76R99 Diffusion and convection (fluid mechanics) 76D05 Navier-Stokes equations (fluid dynamics)
KELLEY