Fast Parallel Stability and Resolvent Analysis for Multi-Resolution External Flows

IBLGF-AMR is an incompressible external flow solver combining Lattice Green's Function (LGF), Immersed Boundary (IB) Method, and Adaptive Mesh Refinement (AMR). This method successfully yielded a range of flow simulations, including fully 3D turbulent flow past a sphere, span-wise periodic turbulent flow past a cylinder, and high-fidelity simulations of starting vortex generated by a flat plate undergoing translational and rotational motions. The success of IBLGF-AMR inspired us to leverage the same techniques to devise an efficient formulation of the discretized linearized Navier-Stokes equations (LNSE), which is foundational to a plethora of flow simulation and analysis methods. In this presentation, we will introduce how we combined IB, LGF, AMR, and Fast Multiple Method (FMM) to create a sparse representation of the LNSE. We applied our method to conduct stability and resolvent analysis of a range of problems to demonstrate the accuracy and effectiveness of this method. In the future, we also plan to apply this sparse linearization to solve external incompressible flows using the time-spectral method.