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.