CPCE CPCE Turbulence Modeling & Numerical Methods 2 — Questions and Answers
Question 1: What is 'numerical diffusion' in CFD and how does it typically arise?
- Physical diffusion added intentionally to stabilize the solver
- Artificial smearing of gradients introduced by low-order upwind discretization (Correct answer)
- Diffusion due to high Reynolds number flows
- Errors caused by round-off in floating-point arithmetic
Correct answer: Artificial smearing of gradients introduced by low-order upwind discretization
Numerical diffusion is artificial smearing of flow gradients caused by truncation errors in low-order (e.g., first-order upwind) discretization schemes.
Question 2: In Reynolds-Averaged Navier-Stokes (RANS) simulations, what does the Reynolds decomposition separate the flow variables into?
- Laminar and turbulent components
- Mean and fluctuating components (Correct answer)
- Compressible and incompressible components
- Viscous and inviscid components
Correct answer: Mean and fluctuating components
Reynolds decomposition splits each flow variable into a time-averaged mean component and a fluctuating component, enabling the RANS approach to turbulence modeling.
Question 3: Which iterative solver is widely used in CFD for solving large sparse linear systems arising from pressure-velocity coupling?
- Gaussian elimination
- Conjugate Gradient (CG) method (Correct answer)
- Runge-Kutta method
- Euler explicit scheme
Correct answer: Conjugate Gradient (CG) method
The Conjugate Gradient method and its preconditioned variants are widely used for solving large sparse symmetric linear systems in CFD pressure solvers.
Question 4: What is the purpose of the SIMPLE algorithm in CFD?
- To generate high-quality structured meshes
- To couple the pressure and velocity fields in incompressible flow solvers (Correct answer)
- To apply turbulence model corrections
- To handle compressible shock-capturing
Correct answer: To couple the pressure and velocity fields in incompressible flow solvers
The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm iteratively solves coupled pressure and velocity equations for incompressible flows.
Question 5: In the context of CFD numerical methods, what is 'upwinding'?
- Solving equations only in the upstream direction
- Using information from the upstream side when discretizing convection terms (Correct answer)
- Increasing mesh resolution in the upstream region
- Applying boundary conditions at the inlet only
Correct answer: Using information from the upstream side when discretizing convection terms
Upwinding biases the discretization of convection terms to use values from the upwind (upstream) direction, improving numerical stability by respecting the direction of information propagation.
Question 6: What does 'order of accuracy' refer to in CFD numerical schemes?
- The number of equations solved simultaneously
- The rate at which the numerical error decreases as the grid is refined (Correct answer)
- The number of iterations required for convergence
- The level of turbulence modeling complexity
Correct answer: The rate at which the numerical error decreases as the grid is refined
Order of accuracy describes how rapidly the truncation error decreases as the mesh is refined; a second-order scheme halves the error when the cell size is halved.
CPCE CPCE Turbulence Modeling & Numerical Methods 2
What is 'numerical diffusion' in CFD and how does it typically arise?