CPCE Computational Fluid Dynamics Theory & Principles 4 — Questions and Answers
Question 1: The PISO (Pressure Implicit with Splitting of Operators) algorithm differs from SIMPLE primarily in that it:
- Solves the momentum equation only once per time step
- Performs multiple pressure corrections per time step without inner iterations (Correct answer)
- Uses an explicit time advancement for the pressure field
- Solves pressure on a staggered grid
Correct answer: Performs multiple pressure corrections per time step without inner iterations
PISO performs a predictor and two (or more) corrector steps per time step, making it more suitable for transient flows than SIMPLE's iterative approach.
Question 2: Which type of mesh is most suitable for complex geometries due to its ability to conform to curved boundaries?
- Structured Cartesian mesh
- Unstructured mesh with triangles/tetrahedra (Correct answer)
- Overlapping (Chimera/overset) mesh
- Uniform rectilinear mesh
Correct answer: Unstructured mesh with triangles/tetrahedra
Unstructured meshes with triangular or tetrahedral elements can conform to arbitrarily complex geometries, making them ideal for industrial CFD applications.
Question 3: The 'checkerboard' pressure instability in co-located grid arrangements arises because:
- The time step is too large for the chosen mesh
- Pressure and velocity are evaluated at the same locations, decoupling alternating pressure modes (Correct answer)
- The viscosity is computed using incorrect gradients
- Boundary conditions are not properly imposed
Correct answer: Pressure and velocity are evaluated at the same locations, decoupling alternating pressure modes
On co-located grids, standard central differencing for the pressure gradient does not sense a checkerboard pressure field, allowing spurious oscillatory modes to persist.
Question 4: In Reynolds-Averaged Navier-Stokes (RANS) modeling, the Reynolds stress tensor arises from:
- Time-averaging the nonlinear convective term, yielding correlations of velocity fluctuations (Correct answer)
- Spatial filtering of the pressure gradient
- Linearization of the viscous stress tensor
- Ensemble averaging of the boundary conditions
Correct answer: Time-averaging the nonlinear convective term, yielding correlations of velocity fluctuations
Time-averaging the nonlinear u·∇u term produces the Reynolds stress tensor −ρ⟨u'u'⟩, which must be modeled to close the RANS equations.
Question 5: The wall-y⁺ parameter is used to determine whether:
- The mesh is fine enough to resolve the viscous sublayer or if wall functions should be used (Correct answer)
- The turbulence model transition criterion is satisfied
- The CFL condition is met near solid walls
- The pressure is correctly prescribed at no-slip walls
Correct answer: The mesh is fine enough to resolve the viscous sublayer or if wall functions should be used
y⁺ = u_τ·y/ν indicates the location of the first mesh point in wall units; y⁺ < 5 implies the viscous sublayer is resolved, while y⁺ ≈ 30–300 suits wall functions.
Question 6: Which finite volume concept ensures that the flux leaving one cell face exactly equals the flux entering the adjacent cell?
- Consistency
- Conservativeness (Correct answer)
- Stability
- Boundedness
Correct answer: Conservativeness
Conservativeness is the property that guarantees flux conservation at cell interfaces, which is a fundamental advantage of the finite volume method.
Question 7: The Boussinesq eddy-viscosity hypothesis assumes that Reynolds stresses are:
- Proportional to the square of the turbulent kinetic energy
- Proportional to the mean rate-of-strain tensor via a scalar turbulent viscosity (Correct answer)
- Independent of the mean flow gradients
- Equal to the molecular viscous stresses
Correct answer: Proportional to the mean rate-of-strain tensor via a scalar turbulent viscosity
The Boussinesq hypothesis expresses Reynolds stresses as μ_t times the mean strain rate, analogous to how viscous stresses relate to strain in Newtonian fluids.
CPCE Computational Fluid Dynamics Theory & Principles 4
The PISO (Pressure Implicit with Splitting of Operators) algorithm differs from SIMPLE primarily in that it: