Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Abstract:

Spanwise periodic incompressible external flows are used to model the flows generated by moving immersed bodies with infinitely long spans and constant cross-sections. They are ubiquitous in science and engineering applications. In this thesis, we propose algorithms to simulate and analyze this type of flow using the lattice Green's functions (LGF), which are the analytical inverse of discrete elliptic operators. These algorithms not only accurately capture the small-scale flow features but also respect the far-field boundary conditions. Using the LGFs, we are able to create numerical algorithms that can accurately simulate and analyze external flows with snug computational domains. By combing LGFs with adaptive mesh refinement (AMR) and immersed boundary (IB) methods, we present two numerical algorithms specially designed for spanwise periodic incompressible external flows: one to simulate this type of flow and one to compute stability and resolvent analysis problems for this type of flow.

In these algorithms, the LGFs of the screened Poisson equation are needed and have to be computed during runtime. To enable efficient flow simulation and analysis algorithms, we propose fast numerical algorithms to tabulate these LGFs and derive their convergence properties and computational complexities. We showed that our algorithms are orders of magnitude faster than existing algorithms when evaluating these LGFs.

Equipped with the fast algorithms for LGFs, we proposed two algorithms: a flow simulation algorithm and a stability and resolvent analysis algorithm, both based on LGFs and designed for spanwise periodic incompressible external flows. In this thesis, we describe these algorithms in detail. In addition, we verify and validate these algorithms through a series of numerical experiments.

In addition, we present three applications of these algorithms. We first use the flow simulation algorithm to validate the starting vortex theory proposed by Pullin and Sader (2021). We then use the flow simulation algorithm to study the fluctuating lift and drag coefficients of the flow past a circular cylinder. Finally, we use the stability analysis algorithm to study the stability characteristics of the flow past a rotating cylinder with a control cylinder in its wake.