High-precision Multi-moment Constrained Finite Volume Advective Model Study

A two dimensional 3rd order positive-definite conservative advection model on cubed-sphere grid is developed in this paper by using a 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 of degrees of freedom can be obtained by the governing equations.The multi-moment constraints in this novel scheme are imposed at the cell center on the point value,the first and second order derivatives,then a polynomial of 4th degree can be reconstructed in a single cell.The resulting MCV3?UPCC scheme has 3rd order accuracy and assure the exact numerical conservation due to the continuity of the flux function at cell interfaces.The trend that the quasi-uniform spherical grid will be adopted in the development of advection model will be popular in the future.In comparison with traditional latitude–longitude(LAT/LON)grid which has the deficiencies of convergence of meridian lines and the polar singularity,the cubed-sphere grid can easily avoid these problems and has quasi-uniform grid spacing which benefits the local reconstruction of scheme.Thus,we present the newly developed advection scheme based on cubed-sphere grid.To suppress the numerical oscillations and keep the positivity of certain physical quantities,the bound-preserving(BP)limiting projection is introduced into the new MCV3?UPCC scheme,which satisfies the minimum and maximum principle.The new 3rd positive-definite conservative multi-moment transport model on the cubed-sphere grid is built in this paper through the following procedures: firstly starting from one dimensional conservation law,then developing them in the 2D Cartesian system and finally extending to the quasi uniform cubic spherical grid.Furthermore,the newly-built numerical transport model has been validated by the widely used benchmarks standard test on the cubed-sphere grid and has a good numerical accuracy while keeping the conservation and positive-definite.Comparing to other national existing high-order transport models,the MCV3?UPCC transport modelling on cubed-sphere grid has the potential to be applied in the real numerical simulations.