CFD - Basics of CFD Numerics

Question 1

Discretization of the partial differential equations is called_______, and Discretization of the integral form of the equations is called__________.

Answer 1

Finite Differences
Finite Volumes

Anderson CFD, Pg. 123

Question 2

Define discretization.

Answer 2

The process by which a closed form mathematical expression (that has continuous values) Is approximated by analogous but different expressions which prescribe values at only a finite number of discrete points.

Anderson CFD, Pg. 125

Question 3

True or False
A difference quotient is also called a finite difference.

Answer 3

True

Anderson CFD, Pg. 128

Question 4

Numerical solutions can only give answers at discrete points in the domain called ______.

Answer 4

Grid points.

Anderson CFD, Pg. 126

Question 5

True or False
The majority of CFD applications involve numerical solutions on a grid that contains uniform spacing.

Answer 5

True

Anderson CFD, Pg. 126

Question 6

Describe the method of finite differences.

Answer 6

The partial derivatives in the governing equations are replaced by approximate algebraic difference quotients, where the algebraic difference quotients are expressed strictly in terms of the flow field variables at 2 or more discrete grid points.

Anderson CFD, Pg. 127

Question 7

Describe an explicit technique for solving finite difference equations.

Answer 7

In an explicit approach, each difference equation contains only one unknown and therefore can be solved explicitly for this unknown and in a straightforward manner.

Anderson CFD, Pg. 147

Question 8

Describe the “Crank-Nicolson form” as used in the implicit approach to solving finite difference equations.

Answer 8

The crank Nicholson approach uses average properties between levels n and n+1. See Eq. (4.40) on page 148 of the reference.

Anderson CFD, Pg. 148

Question 9

True or False
The Crank-Nicolson formulation results in one equation and one unknown.

Answer 9

False. The Crank-Nicolson form has multiple unknows and requires an implicit approach.

Anderson CFD, Pg. 148

Question 10

Define an implicit approach for solving finite difference equations.

Answer 10

An implicit approach is one where the unknowns must be obtained by means of a simultaneous solution of the difference equations applied at all grid points at a given time level.

Anderson CFD, Pg. 148

Question 11

True or False
For the explicit approach, once a dx is chosen, then dt is not an independent, arbitrary choice; rather, dt is restricted to be equal to or less than a certain value prescribed by a stability criterion.

Answer 11

True

Anderson CFD, Pg. 151

Question 12

True or False
Implicit approaches must be subject to stability criterion in the marching direction to maintain numerical stability.

Answer 12

False.

Anderson CFD, Pg. 151