A class of higher order compact schemes for the unsteady two‐dimensional convection–diffusion equation with variable convection coefficients

TLDR: In this article, a class of higher order compact (HOC) schemes with weighted time discretization for the two-dimensional unsteady convection-diffusion equation with variable convection coefficients was developed.

Abstract: 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 μ and fourth order accurate in space. For 0.5 ≤ μ ≤ 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