A high order positive-definite conservative multi-moment center constrained finite volume transport model

A two dimensional 3rd order positive-definite conservative advection model is developed in this study based on the novel 3-point multi-moment constrained finite-volume scheme for uniform points with center constraints (MCV3_UPCC). In the context of 3-point multi-moment finite volume method, three equidistant solution points are defined within a single cell and the time evolution equations can be obtained by flux form formulation. The multi-moment constraints in this novel scheme are imposed at the cell center on the point value, the first and second order derivatives, and a polynomial of 4th degree can then be reconstructed in a single cell. The resulting MCV3_UPCC scheme has 3rd order accuracy and ensures the exact numerical conservation due to the continuity of the flux function at cell interfaces. To suppress the numerical oscillations and the positivity of certain physical quantities, the bound-preserving limiting projection is introduced into the new MCV3_UPCC scheme, which satisfies the minimum and maximum principle. The new positive-definite conservative advection model is validated by widely used benchmarks. The presented transport model has a good accuracy in comparison with other existing high-order models, and it has the potential to be applied in real moist transport model.