CPCE Computational Fluid Dynamics Theory & Principles 5

Question 1

In Direct Numerical Simulation (DNS), the minimum mesh spacing required scales approximately as:

Accepted Answer

Re^(3/4)

Answer

DNS must resolve down to the Kolmogorov length scale η ~ Re^(-3/4)L, so mesh point counts scale as Re^(9/4) in 3D, making DNS prohibitively expensive at high Re.

Question 2

The Lax-Wendroff scheme achieves second-order accuracy in both space and time by:

Accepted Answer

Replacing the time derivative with spatial derivatives via the PDE itself before discretizing

Answer

Lax-Wendroff substitutes the second time derivative with spatial derivatives using the governing PDE, enabling a single-step second-order scheme.

Question 3

Which boundary condition type specifies the gradient (flux) of a variable normal to the boundary, rather than its value?

Accepted Answer

Neumann condition

Answer

A Neumann boundary condition prescribes the normal derivative (flux) of the variable at the boundary, commonly used for symmetry planes or fully developed outflow.

Question 4

The concept of 'numerical diffusion' as opposed to 'numerical dispersion' refers to:

Accepted Answer

Smearing of sharp gradients caused by truncation error in the dissipative part of the scheme

Answer

Numerical diffusion arises from even-order truncation error terms that act like additional viscosity, smearing gradients, while numerical dispersion comes from odd-order terms causing phase errors.

Question 5

In the Finite Volume Method, the divergence theorem is used to convert the volume integral of a divergence term into:

Accepted Answer

A surface (face) integral of fluxes

Answer

Gauss's divergence theorem converts ∫_V ∇·F dV into ∮_S F·n dS, transforming volume divergence integrals into face flux integrals in FVM.

(CPCE) Certified Professional CFD Engineer Practice Test

(CPCE) Certified Professional CFD Engineer Practice Test

CPCE Computational Fluid Dynamics Theory & Principles 5