High-order accurate bicompact schemes for solving the multidimensional inhomogeneous transport equation and their efficient parallel implementation

Abstract

The method of lines is used to obtain semidiscrete equations for a bicompact scheme in operator form for the inhomogeneous linear transport equation in two and three dimensions. In each spatial direction, the scheme has a two-point stencil, on which the spatial derivatives are approximated to fourth-order accuracy due to expanding the list of unknown grid functions. This order of accuracy is preserved on an arbitrary nonuniform grid. The equations of the method of lines are integrated in time using diagonally implicit multistage Runge–Kutta methods of the third up fifth orders of accuracy. Test computations on refined meshes are presented. It is shown that the high-order accurate bicompact schemes can be efficiently parallelized on multicore and multiprocessor computers.