A finite volume scheme for the convection-diffusion system using the polynomial reconstruction operator

We present a new very high-order finite volume scheme for the two-dimensional convection-diffusion problem system based on the local Polynomial Reconstruction Operator (PRO-Scheme). We detail the design of the schemes and provide an example with regular solution. The solution is presented for Patankar scheme and for PRO scheme. In this last case we present the solution using a polynomial reconstruction of degree 1 and 2.