Simulation of vorticity dominated flows using a hybrid approach. II: Numerical method

✍ Scribed by W. Kollmann

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 617 KB
• Volume: 36
• Category: Article
• ISSN: 0045-7930
• DOI: 10.1016/j.compfluid.2007.03.004

✦ Synopsis

A family of numerical methods for the solution of the incompressible Navier-Stokes equations in cylindrical coordinates is developed. The formulation for hybrid spectral-finite difference discretizations in domains with cylindrical boundaries presented in Kollman, in press [Kollmann W, Simulation of vorticity dominated flows using a hybrid approach: I formulation, in press] forms the basis of the solvers. The solution methods use the Fourier-spectral approach for the azimuthal and a set of finite-difference operators for the radial and axial directions. The convective terms are discretized with a linear combination of upwind-biased and central difference operators applied to the non-conservative and conservative formulations, respectively. All other spatial derivatives are discretized with central operators. The time integration is specified as a minimum storage, state space, fourth order Runge-Kutta method. The convergence of the solvers as the formal accuracy of the finite-difference operators varies is tested for an axi-symmetric flow for fixed discretization and time integrator. The results show satisfactory convergence with respect to order of accuracy and the convective operators.