CPCE Computational Fluid Dynamics Theory & Principles 3 — Questions and Answers
Question 1: Which turbulence model solves two transport equations — one for turbulent kinetic energy and one for its dissipation rate?
- Spalart-Allmaras
- k-ε model (Correct answer)
- Smagorinsky LES model
- Reynolds Stress Model (RSM)
Correct answer: k-ε model
The k-ε model solves transport equations for turbulent kinetic energy k and its dissipation rate ε, making it a two-equation RANS model.
Question 2: The CFL (Courant-Friedrichs-Lewy) condition states that for explicit schemes the time step must satisfy:
- CFL = u·Δt/Δx ≤ 1 (Correct answer)
- CFL = ν·Δt/Δx² ≤ 1
- CFL = Δt/Δx ≥ 1
- CFL = u·Δx/ν ≤ 1
Correct answer: CFL = u·Δt/Δx ≤ 1
The CFL condition CFL = u·Δt/Δx ≤ 1 ensures that information cannot travel more than one cell per time step for explicit convection schemes.
Question 3: In Large Eddy Simulation (LES), the role of the subgrid-scale (SGS) model is to:
- Resolve all turbulent scales including the Kolmogorov scale
- Model the effect of unresolved small-scale eddies on the resolved flow (Correct answer)
- Replace the Navier-Stokes equations with algebraic relations
- Compute pressure corrections at each iteration
Correct answer: Model the effect of unresolved small-scale eddies on the resolved flow
LES explicitly resolves large eddies but models the energy drain from resolved scales to unresolved small eddies via SGS models.
Question 4: The QUICK scheme (Quadratic Upstream Interpolation for Convective Kinematics) is third-order accurate and uses:
- Two upstream and one downstream node for interpolation (Correct answer)
- Only downstream nodes
- Central differencing with flux limiters
- Only the immediate upstream node
Correct answer: Two upstream and one downstream node for interpolation
QUICK fits a quadratic through two upstream and one downstream node to interpolate face values, achieving third-order spatial accuracy.
Question 5: Which statement best describes the concept of 'multigrid' in CFD solvers?
- Using multiple meshes with different element types simultaneously
- Accelerating convergence by solving residual equations on coarser grids (Correct answer)
- Automatically refining the mesh in high-gradient regions
- Partitioning the domain for parallel computation
Correct answer: Accelerating convergence by solving residual equations on coarser grids
Multigrid methods use a hierarchy of coarser grids to efficiently damp error modes of all wavelengths, dramatically accelerating iterative solver convergence.
Question 6: The divergence-free constraint for incompressible flow (∇·u = 0) is enforced in pressure-based solvers by:
- Setting the pressure gradient to zero
- Solving a pressure (or pressure-correction) Poisson equation
- Applying a solenoidal projection to the velocity field
- Both B and C (Correct answer)
Correct answer: Both B and C
Pressure-based incompressible solvers derive a Poisson equation for pressure (or pressure correction) whose solution, when applied to the velocity, projects it onto the divergence-free space.
Question 7: In CFD, 'grid sensitivity study' is performed to:
- Ensure the solver converges in fewer iterations
- Demonstrate that results are independent of mesh resolution (Correct answer)
- Reduce computational cost by coarsening the mesh
- Validate turbulence model constants
Correct answer: Demonstrate that results are independent of mesh resolution
A grid sensitivity (or mesh independence) study verifies that further mesh refinement does not significantly alter key solution quantities, confirming discretization error is acceptable.
CPCE Computational Fluid Dynamics Theory & Principles 3
Which turbulence model solves two transport equations — one for turbulent kinetic energy and one for its dissipation rate?