CFD 2

What is Computational Fluid Dynamics (CFD)

The numerical study of fluid flow and heat transfer using numerical approximations where analytical solutions are impossible

What is the difference between Navier-Stokes (NS) and RANS equations

RANS equations are time-averaged versions of Navier-Stokes that introduce Reynolds stresses to account for turbulence

Why does CFD normally solve RANS instead of the exact Navier-Stokes equations

Resolving all scales of turbulence via exact NS (DNS) is computationally prohibitive for most engineering problems

What is the "closure problem" in turbulence modelling

The averaging process creates more unknowns (Reynolds stresses) than available equations, requiring a model to "close" the system

Define the Boussinesq Hypothesis.

Reynolds stresses are proportional to mean velocity gradients - introduces the concept of eddy viscosity

What are the advantages of the k-omega model

It is superior for boundary layer flows and adverse pressure gradients

Under what flow conditions is a Reynolds Stress Model (RSM) recommended

Flows dominated by complex features like strong swirl, high rotation, or high strain

What are the primary disadvantages of Reynolds Stress Models (RSM)

They require high computational resources and are often difficult to converge compared to eddy viscosity models

What is U+

U+ is the ratio between axial velocity and friction velocity

What are the meshing requirements for a wall-function turbulence model

The first mesh node must be placed in the log-law region, typically between y+ values of 30 and 300

What are the meshing requirements for a wall-resolved (Low-Re) model

The first mesh node must be placed very close to the wall, typically requiring a y+ value less than 1

What is the physical meaning of the Local Derivative

The time rate of change of a fluid property at a fixed point in the flow field

What is the physical meaning of the Convective Derivative

The time rate of change due to a fluid element moving between locations where properties are spatially different

What is the Substantial (Total) Derivative

The sum of local and convective derivatives, representing the rate of change following a moving fluid element

What is the difference between the Finite Difference Method (FDM) and Finite Volume Method (FVM)

FDM is easy to develop for higher orders, but FVM is inherently conservative and better for complex geometries

What are the advantages of Explicit time discretization

It is computationally cheap per step

What are the advantages of Implicit time discretization

It is unconditionally stable for any time step

Define the SIMPLE algorithm.

A predictor-corrector method used in pressure-based solvers to achieve pressure-velocity coupling and ensure mass conservation

What is the purpose of the Under-relaxation Factor in CFD iterations

It moderates the change of variables between iterations to prevent instability or divergence in non-linear equations

What is the aim of a Mesh Independence Study

To ensure the solution does not depend on grid resolution by refining the mesh until results stop changing significantly

How is the quality of a computational mesh measured

Mesh quality is assessed using traits such as skewness, aspect ratio, smoothness, and flow alignment

What is verification

Ensuring the equations are solved correctly (code check)

What is the difference between Newtonian and non-Newtonian fluids

Newtonian fluids have a constant viscosity; non-Newtonian fluids have a viscosity that varies with the shear rate

What is the 0.3 Rule regarding Mach number in solver selection

Flow is typically treated as incompressible for Mach numbers below 0.3 using pressure-based solvers.

Compare the memory usage and convergence of Segregated and Coupled solvers

Segregated solvers use less memory but converge slowly while Coupled solvers use more memory but converge much faster for complex physics.

What is the truncation error in the context of discretization

It is the difference between the exact analytical derivative and its finite-difference approximation.

What does the order of accuracy signify for a numerical scheme

It describes how rapidly the truncation error decreases as the computational grid is refined and the spacing is reduced.

What are the primary advantages of Direct Methods for solving equations

They provide an exact solution

Why are iterative methods used instead of direct methods in CFD packages

Iterative methods are much more memory-efficient and faster for solving the large, linearised algebraic systems produced by discretization.

What are the advantages of the QUICK convection scheme

It provides high-order accuracy on uniform meshes

What is the physical meaning of the diffusion term in a transport equation

It represents the transport of fluid properties caused by molecular or turbulent mixing.

What are the differences between standard and non-equilibrium wall functions

Non-equilibrium wall functions are more accurate for complex flows because they account for the effects of pressure gradients.

What is the physical meaning of the source term in the momentum equation

It represents the pressure gradient, which acts as the forcing mechanism providing energy for the fluid to flow.

What is the transportiveness property of a numerical scheme

The ability of a scheme to account for the direction of fluid flow, ensuring information travels in the direction of velocity.

What is the purpose of using Algebraic Multigrid (AMG) in iterative solvers

AMG addresses low-frequency global errors by transferring the problem to successively coarser meshes to accelerate convergence.

For which specific applications was the Spalart-Allmaras (SA) turbulence model designed

It was designed specifically for aerospace applications involving wall-bounded flows and boundary layers with adverse pressure gradients.

How does the Reynolds Stress Model (RSM) close the RANS equations

It solves additional transport equations for all six independent Reynolds stresses rather than using an eddy viscosity assumption.

What is the primary purpose of the pressure correction equation in CFD solvers

It is used to restore continuity and ensure mass conservation for the calculated velocity field.

Which action cannot be used to overcome a simulation that oscillates and does not converge

Reducing the convergence tolerance

Why is time dependence in fluid flow problems considered purely parabolic

Because any forcing introduced only affects the future and never the past, allowing solution methods to march in time.

What is the order of accuracy for the Crank-Nicolson time integration scheme

It is an implicit method that provides second-order accuracy in time using the trapezium rule.

Why should high aspect ratio grid cells be avoided in regions where flow is developing

They can adversely influence convergence and solution accuracy because flow features must be adequately resolved in multiple dimensions.

What is the difference between Jacobi and Gauss-Seidel iterative methods

Jacobi uses values from the previous iteration for all nodes while Gauss-Seidel uses the latest available values from the current sweep.

What complex flow features can Reynolds Stress Models (RSM) predict more accurately than eddy viscosity models

RSM accurately accounts for streamline curvature, swirl, rotation, and high strain rates.

Which property is negatively affected if the convergence tolerance value is set too large

Accuracy

What is a known weakness of the Spalart-Allmaras one-equation model

It cannot rapidly accommodate changes in length scale when flow abruptly changes from wall-bounded to free shear.

What is the Eulerian approach to fluid motion

It monitors flow properties at a fixed point in space while the fluid moves through it.

What is the standard first aid step if an iteration begins to diverge

Lowering the under-relaxation factors for pressure and momentum is the standard step to stabilize the simulation.

What is the stagnation point anomaly in turbulence modelling

It is the tendency of eddy-viscosity models to overestimate turbulence production in regions of high strain.

How does a coupled solver differ from a segregated solver regarding the energy equation

In a coupled solver, the continuity, momentum, and energy equations are solved together simultaneously rather than sequentially.

What does a Péclet number of one indicate in a convection-diffusion problem

It indicates that the convective transport and diffusive transport are of equal magnitude in the flow.

Why does refining the mesh often require a reduction in the time step

A smaller mesh size decreases the cell length, which requires a smaller time step to keep the CFL number within stable limits.

What is the physical meaning of the Kronecker delta in the Reynolds stress tensor

It is a tensor that equals one if indices match and zero otherwise, ensuring the term only applies to normal turbulent stresses.

What are the advantages of the Standard k-epsilon model

Robustness and economy for simple flows

What are disadvantages of the Standard k-epsilon model

Poor performance for swirling or strongly separated flows

What are disadvantages of the k-omega model

Sensitive to free-stream boundary conditions

What is y+

y+ is a non-dimensional wall distance used for mesh resolution

What are disadvantages of Explicit time discretization

Only conditionally stable, requiring a CFL number less than 1

What are disadvantages of Implicit time discretization

More expensive per step because it requires iterations

What is validation

Ensuring the right equations are solved (physics check)

What are disadvantages of Direct Methods for solving equations

They are computationally prohibitive for the large systems of equations found in CFD.

What are disadvantages of the QUICK convection scheme

Can lack boundedness and cause numerical oscillations on non-uniform grids.

What is the Stokes relationship

Relationship between viscous stresses, and velocity gradients