3 credits
Spring 2025 Lecture Distance Learning Upper DivisionFinite difference methods for solving fluid flow problems. Review of classification of partial differential equations, well-posed problems, and discrete approximation of partial differential equations. Matrix and von Neumann stability analysis. Consistency and convergence. Grid generation: elliptic, hyperbolic, and transfinite mesh generation methods. Methods for solving the unsteady Euler equations: finite-volume formulations, flux-split and flux-difference formulations, shock-capturing, formulation of boundary conditions, artificial viscosity models, and multi-grid acceleration.
Learning Outcomes1Select and construct solution algorithms for ODEs and PDEs encountered in aerospace and mechanical engineering based on understanding of flow physics and capability of numerical methods.
2Select and construct solution algorithms for flows that may be modeled as viscous or inviscid, compressible or incompressible and choose appropriate initial and boundary conditions.
3Explain consistency, stability, and convergence of numerical methods for PDEs and how they affect the accuracy of numerical solutions.
4State and explain factors that affect accuracy of computed solutions generated by research and commercial CFD codes and how errors could be assessed and minimized.
5State and explain limitations of CFD analysis because of assumptions invoked and uncertainties in models and inputs.