High-order approximation of 2D convection-diffusion equation on hexagonal grids

We derive a fourth-order finite difference scheme for the two-dimensional convection-diffusion equation on an hexagonal grid. The difference scheme is defined on a single regular hexagon of size h over a seven-point stencil. Numerical experiments are conducted to verify the high accuracy of the derived scheme, and to compare it with the standard second-order central difference scheme.