

1. Mathematical Description of Physical PhenomenaGoverning equations  mass, momentum, energy, speciesGeneral form of the scalar transport equation Elliptic, parabolic and hyperbolic equations Behavior of the scalar transport equation with respect to these equation types 2. Overview of Numerical MethodsMesh terminology and typesMethods for deriving discretization equations Methods for solving discretization equations Accuracy, consistency, stability and convergence 3. Diffusion EquationDiscretization of conduction equationSource terms, nonlinearity Boundary conditions Underrelaxation Solution of linear equations (preliminary) Other coordinate systems Unsteady conduction Twodimensional conduction on unstructured meshes Accuracy, stability and convergence revisited 4. Convection and DiffusionSteady onedimensional convection and diffusionUpwind scheme Twodimensional convectiondiffusion Accuracy of upwind scheme; false diffusion Higherorder schemes Boundary conditions Generalization to unstructured meshes 5. Linear SolversGaussSeidel schemeTridiagonal matrix algorithm (TDMA), lineiterative solvers Multigrid methods and application to unstructured meshes Conjugate gradient methods 6. Flow Field CalculationIncompressibility issues and pressurevelocity couplingPrimitive variables versus other methods Staggered grid for structured meshes SIMPLE family of algorithms Nonstaggered mesh methods Bodyfitted formulations Unstructured mesh formulation 7. Projects 