Nonlinear dynamics for the 3D ideal viscous gas flow over the cylinder

Abstract

The system of governing equations for the dynamics of the compressible viscous ideal gas is considered in the 3D bounded domain with the inflow and outflow boundary conditions. The cylinder is located in the domain. Such problem is simulated using the high order WENO-scheme for inviscid part of the equations and using 4-th order central approximation for the viscous tensor part with the third order temporal discretization.The method of Proper Orthogonal Decomposition (POD) is applied to the problem at hand in order to extract the most active nodes. Cascades of bifurcations of periodic orbits and invariant tori are found that correspond to the excitation in different POD modes. The approximation of the reduced order model is analyzed and it is shown that one cannot make parameter extrapolations for the reduced order model to capture the same dynamics as is observed in the original full size model.