# Undergraduate and Graduate Courses

## AER336: Scientific Computing## Course DescriptionA first introduction to numerical methods for scientific computation relevant to engineering problems. Topics addressed include interpolation, integration, linear systems, least-squares fitting, nonlinear equations and optimization, initial value problems, partial differential equations, and relaxation methods. Tutorials and assignments make extensive use of MATLAB. Assignments also require knowledge of Fortran, C, or C++. |
## AER310: Gasdynamics## Course DescriptionBasic introduction to compressible gasdynamics. Includes some fundamental thermodynamics, thermal and caloric equations of state, derivation of Eulerâ€™s equations by control volume approach. Also, includes the theory of steady flows in ducts with area changes, adiabatic frictional flows, duct flows with heat transfer, normal and oblique shock waves, Prandtl-Meyer expansion wave, moving shock and rarefaction waves, shock tubes, and wind tunnels. The lectures are supplemented by problem sets. Reference book: Anderson, J.D., Modern Compressible Flow with Historical Perspective. |

## AER1301: Kinetic Theory of Gases## Course URL:arrow.utias.utoronto.ca/~groth/aer1301 ## Course DescriptionIntroductory discussion of significant length dimensions; different flow regimes, continuum, transition, collision-free; and a brief history of gas kinetic theory. Equilibrium kinetic theory; the article distribution function; Maxell-Boltzmann distribution. Collision dynamics; collision frequency and mean free path. Elementary transport theory, transport coefficients, mean free path method. Boltzmann equation; derivation, Boltzmann H-theorem, collision operators. Generalized transport theory; Maxwell's equations of change; approximate solution techniques, Chapman -Ensog perturbative and Grad series expansion methods, moment closures; derivation of the Euler and Navier-Stokes equations, higher-order closures. Free molecular aerodynamics. Shock waves. |
## AER1310: Turbulence Modelling## Course URL:arrow.utias.utoronto.ca/~groth/aer1310 ## Course DescriptionOverview of numerical modelling techniques for the prediction of turbulent flows with emphasis on the capabilities and limitations of engineering approaches commonly used in computational fluid dynamics (CFD) for the simulation of turbulence. Topics include: Introduction to turbulent flows; definition of turbulence; features of turbulent flows; requirements for and history of turbulence modeling. Conservation equations for turbulent flows; Reynolds and Favre averaging; velocity correlations, Reynolds-averaged Navier-Stokes equations (RANS); Reynolds stress equations; effects of compressibility. Algebraic Models; eddy viscosity and mixing length hypothesis; Cebeci-Smith and Baldwin-Lomax models. Scalar-field evolution models; turbulence energy equation; one- and two-equation models; wall functions; low-Reynolds-number effects. Second-order closure models; full Reynolds-stress and algebraic Reynolds stress models. Large-Eddy Simulation (LES) techniques. Direct Numerical Simulation (DNS) Methods. |

## AER1319: Finite Volume Methods for CFD## Course URL:arrow.utias.utoronto.ca/~groth/aer1319 ## Course DescriptionIntroduction to upwind finite-volume methods widely used in computational fluids dynamics (CFD) for thehe solution of high-speed inviscid and viscous compressible flows. Topics include: Brief review of conservation equations for compressible flows; Euler equations; Navier-Stokes equations; one- and two-dimensional forms; model equations. Mathematical properties of the Euler equations; primitive and conserved solution variables; eigensystem analysis; compatibility conditions; characteristic variables, Rankine-Hugoniot conditions and Riemann invariants; Riemann problem and exact solution. Godunov's method; hyperbolic flux evaluation and numerical flux functions; solution monotonicity; Godunov's theorem. Approximate Riemann solvers; Roe's method. Higher-order Godunov-type schemes; semi-discrete form; solution reconstruction including least-squares and Green-Gauss methods; slope limiting. Extension to multi-dimensional flows. Elliptic flux evaluation for viscous flows; diamond-path and average-gradient stencils; discrete-maximum principle. High-order methods; essentially non-oscillatory (ENO) schemes. |
## AER510: Aerospace Propulsion## Course DescriptionScope and history of jet and rocket propulsion; fundamentals of air-breathing and rocket propulsion; fluid mechanics and thermodynamics of propulsion including boundary layer mechanics and combustion; principles of aircraft jet engines, engine components and performance; principles of rocket propulsion, rocket performance, and chemical rockets; environmental impact of aircraft jet engines. |