## Chapter 12

The Time-Marching Technique

## The Time-Marching Technique

### Overview

### Chapter Roadmap

### Study Guide

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

- Explain the concepts zone of influence and zone of dependence?
- Describe in words how a finite-volume spatial discretization can be achieved.
- Which equations are suitable to use when deriving a finite-volume spatial discretization for compressible flow?
- What is meant by the term
*density-base*when discussing CFD codes for compressible flow? - What is meant by the term
*fully coupled*when discussing CFD codes for compressible flow? - 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?
- Derive a third-order upwind scheme using a four-cell stencil.
- What do we mean when we say that a CFD code for compressible flow is conservative?
- Why is it important that a CFD code for compressible flow is conservative?
- 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.
- What is a typical maximum CFL number for stable operation when applying an explicit time stepping scheme?
- How can we use our knowledge of characteristics (and their speed of propagation) to guide us when determining suitable boundary conditions for compressible flows?
- 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?
- 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.*