Syllabus
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1. Mathematical Description of Physical Phenomena

Governing equations -- mass, momentum, energy, species
General 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 Methods

Mesh terminology and types
Methods for deriving  discretization equations
Methods for solving discretization equations
Accuracy, consistency, stability and convergence

3. Diffusion Equation

Discretization of conduction equation
Source terms, non-linearity
Boundary conditions
Under-relaxation
Solution of linear equations (preliminary)
Other coordinate systems
Unsteady conduction
Two-dimensional conduction on unstructured meshes
Accuracy, stability and convergence revisited

 4. Convection and Diffusion

Steady one-dimensional convection and diffusion
Upwind scheme
Two-dimensional convection-diffusion
Accuracy of upwind scheme; false diffusion
Higher-order schemes
Boundary conditions
Generalization to unstructured meshes

5. Linear Solvers

Gauss-Seidel scheme
Tri-diagonal matrix algorithm (TDMA), line-iterative solvers
Multi-grid methods  and application to unstructured meshes
Conjugate gradient methods

6. Flow Field Calculation

Incompressibility issues and pressure-velocity coupling
Primitive variables versus other methods
Staggered grid for structured meshes
SIMPLE  family of algorithms
Non-staggered mesh methods
Body-fitted formulations
Unstructured mesh formulation

7. Projects