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High‐order finite volume schemes for the advection–diffusion equation

A high‐order finite volume method based on piecewise interpolant polynomials is proposed to discretize spatially the one‐dimensional and two‐dimensional advection–diffusion equation. Evolution equations for the mean values of each control volume are integrated in time by a classical fourth‐order Runge–Kutta. Since our work focuses on the behaviour of the spatial discretization, the time step is chosen small enough to neglect the time integration error.