Shape-preserving multimoment scheme for advection transport on a hexagonal grid

A shape-preserving multimoment scheme is designed to solve the advection equation on a hexagonal grid. Two types of local degrees of freedom are defined, including a volume-integrated average and six point values for each cell. A quadratic reconstruction polynomial is constructed using a single-cell stencil to implement a third-order scheme. A flux-correction algorithm is proposed for shape-preserving simulations. By adjusting the mass leaving a cell through modifying the point values, the solution of volume-integrated average can preserve the local extreme values in non-divergent flows. A smoothness indicator based on the weighted essentially non-oscillatory concept is adopted to avoid losing accuracy in smooth regions. The proposed scheme is checked by widely used benchmark tests, and numerical results demonstrate that it has third-order accuracy on the planar and spherical hexagonal grids and is free of non-physical oscillations around discontinuities. The proposed scheme has the practical potential to build accurate and scalable advection equation solvers on various spherical polygonal grids for atmospheric general circulation models.