Computational Fluid Dynamics

Project Requirements -

-Create a code to solve the problem using explicit formulation.

-Perform a grid-refinement study. Start with 41x41 grid and refine until results at least.

• I recommend refining by "doubling" the nodes in each direction (81, 161, etc)

-Explore the effects of time-derivative preconditioning by varying k (slide 14).

• Select the best value for each grid size. Baseline k =0.1

-Explore the effects of artificial viscosity by varying C⁽⁴⁾. Note that it may need to be negative.

• I recommend varying it as 1/(powers of 2) (1/16, 1/32, 1/64, etc).
• Select the best value for each grid size. Baseline C⁽⁴⁾ = 0.0625

-Explore the effects of local vs global time stepping. How are stability and number of iterations affected?

• Try to minimize the number of iterations by varying k, C⁽⁴⁾, CFL, and local vs. global time stepping.

-Compare results to those from a commercial code, such as Fluent or OpenFOAM

-Run the code for Reynolds number 100, 200, 400 and compare physical results.

Report Requirements -

-Introduction and Problem Statement

-Governing Equations

• Present the continuous physics equations that govern the flow
• Include a discussion of the mathematical character and explain why we are using Time-Derivative Preconditioning

-Discretization Approach

• Present the discretized equations, order of accuracy
• Include a discussion of odd-even pressure/velocity decoupling and explain why we are using Artificial Viscosity

-Steady-State Convergence

• Present the convergence criteria and how you calculate them at each timestep.

Attachment:- Assignment.rar