Compact grid-characteristic schemes of higher orders for 3D linear transport equation

A numerical solution of 3D linear transport equation on parallelepiped grids is described. With the usage of split along coordinate axis technique compact grid-characteristic schemes of higher orders were generalized up to 3D case. The influence of separate steps of the algorithm on the precision of the final scheme was estimated. The approach for preserving the convergence order of scheme on smooth solution and minimize unphysical oscillations on discontinuous solution in 3D was proposed.