Direct Numerical Simulation of a Compressible Flow and Matrix-Free Analysis of its Instabilities over an Open Cavity

Abstract

This study takes a Jacobian-free approach based on the Arnoldi iteration to present a method to perform hydrodynamic instability analysis based on Direct Numerical Simulations. The method employs high order spatial and temporal discretizations for the flow simulation and has very low requirements of computational time and memory, compared to conventional matrix-forming methods. Details of the numerical treatment applied to guarantee consistency in the numerical solution are discussed, such as mesh and domain dependencies, and buffer zones for the open boundary conditions. The implementation presented here is applicable to any flow with Cartesian geometry, however, the method can be extended to complex geometries and three-dimensional flows.