Computational Aerodynamics
AAE51200
Credit Hours:
3Learning Objective:
Be able to select and construct solution algorithms for ODEs and PDEs encountered in aerospace and mechanical engineering based on understanding of flow physics and numerical methods. Be able to select and construct solution algorithms for flows that may be modeled as viscous or inviscid, compressible or incompressible, and choose appropriate initial and boundary conditions. Be able to explain consistency, stability, and convergence of numerical methods for PDEs and how they affect the accuracy of numerical solutions. Be able to state and explain factors that affect accuracy of computed solutions generated by research and commercial CFD codes and how errors could be assessed and minimized. Be able to state and explain limitations of CFD analysis because of assumptions invoked and uncertainties in models and inputs.Description:
This course provides an introduction to finite-difference (FD) and finite volume (FV) methods in CFD. The course is divided into three parts. Part 1 reviews the building blocks needed to develop, analyze, and implement CFD, including methods for initial and boundary-value problems, methods for linear and nonlinear algebraic equations, classification and properties of partial differential equations (PDEs), and the equations that govern fluid mechanics, heat transfer, and combustion problems. Part 2 presents FD and FV methods in a step-by-step manner, showing how the building blocks are assembled and their limitations. These include mapping of coordinate systems, grid generation, FD and FV operators, and methods of analysis for consistency, stability, convergence, and errors such as conservation, transportive, dissipation, dispersion, aliasing, and lack of monotonicity and positivity. Part 3 shows how FD and FV methods are applied to the Euler and the Navier-Stokes equations for compressible and incompressible flows with focus on boundary conditions, verification and validation issues, and uncertainty quantification.