High-order and high-resolution schemes with generalized characteristic boundary conditions for computational aeroacoustics of unsteady compressible flows

Abstract

The optimized high-order compact (OHOC) finite difference schemes are proposed as the central schemes at the interior nodes and the non-central or one-sided schemes at and near the boundary nodes for aeroacoustic computations. The high-order compact schemes are optimized in the wavenumber domain by using Fourier error analysis. Analytic optimization methods are devised to minimize the dispersion and the dissipation errors and obtain maximum resolution characteristics of the high-order compact schemes. With the accurate finite difference schemes in space, the high-order Runge-Kutta scheme is employed for the integration of numerical solutions in time. The feasibility of applying the artificial dissipation algorithm and implementing the physical boundary conditions for the high-order and high-resolution schemes are investigated to provide high-quality aeroacoustic solutions. An adaptive nonlinear artificial dissipation model is proposed for CAA to enhance the numerical stability and convergence of the OHOC schemes based on the central differences. The generalized characteristics boundary conditions are presented for the actual CAA with the high-order and high-resolution schemes in the domain surrounded by the non-reflecting inflow/outflow with transparent acoustic sources and slip/no-slip solid wall boundaries. An improved artificial dissipation model is presented for performing aeroacoustic computations by the high-order and high-resolution numerical schemes based on the central finite differences. The artificial dissipation model for CAA is able to damp out the spurious oscillations generated by nonlinear discontinuous waves only, while keeping the linear acoustic waves unaffected. In this thesis, an effective formalism of adaptive nonlinear artificial dissipation model is presented by combining the artificial selective damping term and a well-established nonlinear shock-capturing term, which is for the temporal accuracy as well as the numerical stability. It i...