COMPUTATION OF UNSTEADY SWIRLING FLOWS IN NOZZLES AND PIPES BY APPLYING A NEW LOCALLY IMPLICIT GODUNOV-TYPE SCHEME

A new class of numerical schemes for calculating unsteady swirling flows in nozzles and pipes based on compressible inviscid gas equations is presented. The main advantage of these schemes is their ability to efficiently handle unsteady problems with multiple scales. The construction of such schemes is based on the well-known Godunov approach, which involves calculating fluxes at the faces of computational cells (volumes) by solving auxiliary one-dimensional problems in the vicinity of each face and approximating conservation laws. The scheme switches from an explicit method to an implicit one for flux calculation based on an analysis of the current solution near the cell face. The scheme is absolutely stable and does not generate spurious oscillations. Its effectiveness is demonstrated in the calculation of unsteady swirling flows in nozzles and pipes. Specifics of setting up problems of this type are investigated, and options for proper problem formulation are proposed. Properties of the solution for swirling flows with a central body covering only part of the symmetry axis in the computational domain are also studied.