Fall 2013

Mesh and Time-Step Independent Computational Fluid Dynamics (CFD) Solutions

Justin J. Nijdam

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common finite-volume method. They conduct a sensitivity analysis to prove their solutions are mesh and time-step independent. The explicit and fully implicit discretization schemes are compared to demonstrate the vulnerability of the former to numerical stability issues. Finally, the students verify the numerical solution by comparison with the analytical solution. The assignment helps students become familiar with CFD methodology and gives them an insight into how commercial CFD solvers work.

KEY WORDS: computational fluid dynamics; CFD; numerical methods; verification; validation

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