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

Аннотация

A numerical solution of a 3D linear transport equation on parallelepipedic computational grids is considered. By the technique of splitting in coordinates, compact grid-characteristic schemes of higher orders of accuracy are generalized to the 3D case. The influence of particular steps of the computational algorithm on the accuracy of the resulting scheme is investigated. The approach for retaining the order of convergence of a scheme on a smooth solution and minimizing nonphysical oscillations on a discontinuous solution in the 3D case is proposed.