## Chapter 12

The Time-Marching Technique

## The Time-Marching Technique

### Study Guide

The questions below are intended as a "study guide" and may be helpful when reading the text book.

1. Explain the concepts zone of influence and zone of dependence?
2. Describe in words how a finite-volume spatial discretization can be achieved.
3. Which equations are suitable to use when deriving a finite-volume spatial discretization for compressible flow?
4. What is meant by the term density-base when discussing CFD codes for compressible flow?
5. What is meant by the term fully coupled when discussing CFD codes for compressible flow?
6. When the governing equations are discretized using a finite-volume approach, cell face values of flow properties appears in the equations. How are these values approximated?
7. Derive a third-order upwind scheme using a four-cell stencil.
8. What do we mean when we say that a CFD code for compressible flow is conservative?
9. Why is it important that a CFD code for compressible flow is conservative?
10. When applying a time-marching flow solution scheme the so-called CFL number is an important parameter. Define the CFL number and describe its significance.
11. What is a typical maximum CFL number for stable operation when applying an explicit time stepping scheme?
12. How can we use our knowledge of characteristics (and their speed of propagation) to guide us when determining suitable boundary conditions for compressible flows?
13. When applying a CFD code for unsteady compressible flow, which of the following choices would you make: density based or pressure based, fully coupled or segregated, conservative or non-conservative, explicit or implicit time stepping?
14. An engineer wants to apply a numerical solution scheme for compressible flow. The flow he is interested in contains shocks. He has to choose between two different solution methods - one which is based on the conservation form of the governing equations and one which is based on the non-conservation form of the governing equations. Which method should he choose and why?
Hint: go through the lecture notes for Chapter 6.