A new very high-order finite volume method for the 2D convection diffusion problem on unstructured meshes

We present a new finite volume scheme based on the Polynomial Reconstruction Operator (PRO-scheme) for the linear convection diffusion problem with structured and unstructured meshes. We first design the numerical scheme for generic two-dimensional cells and introduce two kinds of polynomial reconstructions. Numerical experiences are carried out to prove the stability and the effectiveness of the method where a 6th-order convergence is reached.FEDER Funds through Programa Operacional Factores de Competitividade — COMPETEFundação para a Ciência e a Tecnologia (FCT) - Projeto PEst-C/MAT/UI0013/2011, projeto PTDC/MAT/121185/201