Abstract:
High-precision bicompact schemes are considered for the multidimensional convection-diffusion equation with constant coefficients. A new implementation of these schemes on regular Cartesian grids is constructed on the basis of a single replacement of dependent variables and a simplified statement of boundary conditions. Unlike the earlier used implementation, it is a multidimensional running counter that allows you to interpolate the desired functions on the edges and faces of cells “on the fly” that is, in the process of traversing the latter. Due to this property, the new implementation is generalized to hierarchical Cartesian meshes with local adaptive thickening depending on the solution. The results of testing the computational algorithm in wide ranges of the Courant number and the number of adaptation levels are presented, which demonstrate high third-order accuracy.
Key words:convection-diffusion equation, compact schemes, bicompact schemes, cartesian grids, adaptive grid grinding, high order of accuracy.
