Computation of unsteady swirling flows in nozzles and pipes by applying a new locally implicit Godunov-type scheme

A numerical scheme of new class is presented for computing unsteady swirling flows in nozzles and pipes based on equations for a compressible inviscid gas. The main advantage of such schemes is that they are efficient as applied to unsteady multiscale problems. A scheme of this type is constructed using Godunov’s well-known approach, according to which fluxes on faces of mesh cells (volumes) are computed by solving auxiliary one-dimensional problems near each face and by approximating conservation laws. An analysis of the current solution near the face is used to switch between explicit and implicit flux computation algorithms. The scheme is unconditionally stable, and it does not generate spurious oscillations. The performance of the scheme is demonstrated by computing unsteady swirling flows in nozzles and pipes. The features of the formulation of problems of this type are investigated, and variants of correct problem formulation are proposed. The properties of solutions of the swirling flow problem with a central body covering part of the axis of symmetry in the computational domain are studied.