Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm

In this article, the wave propagation properties of the 1D spectral volume method are studied through analysis of the Fourier footprint of the schemes. A p-multigrid algorithm for the spectral volume method is implemented. Restriction and prolongation operators are discussed and the efficiency of the smoothing operators is analyzed. The results are verified for simple 1D advection problems and for a quasi-1D Euler flow. It is shown that a significant decrease in computational effort is possible with the p-multigrid algorithm.