The conventional spectral volume (SV) method for three-dimensional tetrahedral unstructured meshes is extended to use hybrid unstructured meshes comprised of tetrahedral, prismatic and hexahedral cells. This extended SV method is named as SV~+ method. In the test calculation of turbulent boundary layer flow over a flat plate, the computational time per one time step using the hybrid mesh is found to be almost halved. In addition, the convergence rate is drastically improved because skewed tetrahedral cells no longer exist in the boundary layer region. Furthermore, a hierarchical subdivision of hexahedral cells enables to incorporate adaptive mesh refinement (AMR) and h-multigrid approach into the present SV~+ method. In order to show the capability of the present SV~+ method in AMR mode, typical test problems of the steady flowfield over a OAT15A airfoil and also the unsteady vortical transport problem are solved. It is shown that the spatial accuracy of the present SV~+ method is well retained for these test problems even when hanging nodes appear in the computational mesh. It is also shown that the convergence rate for solving a diffusion equation is drastically improved by utilizing hp-multigrid in the present SV~+ method.
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