# Computational Methods in Transport
Phenomena I

##
Mech 510

### Instructor: Carl Ollivier-Gooch

My research interests are in algorithms for
flow solution on unstructured meshes, algorithms for unstructured mesh
generation, and aerodynamic shape optimization. I’m happy to discuss
any of these topics (or just about anything else related to CFD or
fluids in general) at length.

Office: CEME 2064.

Phone: 822-1854.

Email:
cfog@mech.ubc.ca

### Class meetings: MWF 2-3, CEME Annex 102

### Marking

25% | Three homework assignments. |

35% | Three programming assignments. |

40% | Final project (due during the final exam period). |

### Programming

This
is a computational fluid dynamics
course, so there is a significant
programming component to the course. You should be comfortable with
some compiled language
(C, Fortran, Pascal, etc).
No, Matlab is not an acceptable substitute.

### Topics Covered

- Introduction. Strengths
of analytical, computational, and experimental methods in fluid
mechanics. Example of CFD development process. Model problems.
- Space discretization techniques.
Summary of finite difference, finite element, and finite
volume approaches. Detailed basis of the finite volume method. Accuracy
analysis and accuracy
assessment based on numerical results.
- Time discretization and stability. Time accuracy analysis for
ODE’s. Stability analysis of
discretized PDE’s. Explicit and implicit time advance methods.
- Finite-volume discretization of Poisson’s equation. Flux evaluation and boundary
conditions. Direct and iterative solution schemes.
- Finite-volume discretization of the wave equation. Upwind flux evaluation.
Physical and
numerical boundary conditions. Explicit time advance schemes applied to
the wave
equation.
- Application problem: Incompressible energy equation. Discretization in space and
time.
Time advance methods. Boundary conditions. Validation.
- Application problem: Laminar Navier-Stokes equations. Computational formulation,
discretization in time and space. Boundary conditions. Implicit time
advance for systems of
equations. Validation techniques for CFD codes.

### Links