A 4th-order and single-cell-based advection scheme on unstructured grids using multi-moments

This paper presents a 2D conservative scheme on triangular meshes for advection transport problem. Different from the conventional finite volume method (FVM), the present scheme uses and carries forward in time not only the cell-integrated average but also the point values at the vertices and Gaussian points at the boundary as the model variables for each triangular element. Treating all these quantities, which are generically called the 'moments' of the physical variable herein, as the prognostic variables enables us to construct more accurate spatial discretization with less computational stencils. Moreover, the resulting numerical scheme appears much more robust to various triangular unstructured meshes. A 4th-order accuracy is achieved by using a cubic polynomial constructed over a single triangular mesh element. The accuracy and the robustness of the proposed method are evaluated by numerical experiments with comparisons to other existing schemes.