A Family of Fourth Order Difference Schemes on Rotated
Grid for Two Dimensional Convection-Diffusion Equation
Jun Zhang, Jules Kouatchou and Lixin Ge
We derive a family of fourth order finite difference schemes on the
rotated grid for the two dimensional convection diffusion equation
with variable coefficients. In the case of constant convection
coefficients, we present an analytic bound on the spectral radius
of the line Jacobi iteration matrix in terms of the cell Reynolds
numbers. Our analysis and numerical experiments show that the proposed
schemes are stable and produce highly accurate solutions.
Classical iterative methods with these schemes are convergent with
large values of the convection coefficients. We also compare the
fourth order schemes with the nine point scheme obtained from the
second order central difference scheme after one step of cyclic reduction.