Synopsis
Explore how different numerical schemes solve gas-dynamics equations, with practical comparisons and concrete results.
This book surveys a range of finite-difference methods used to simulate conservation laws. It explains how each scheme works, where it performs well, and where it struggles with shocks, rarefactions, or discontinuities. The discussion includes both classic methods and corrective techniques, plus implementation notes and performance insights.
- How Godunov, Lax-Wendroff, MacCormack, and Rusanov differ in accuracy and behavior near sharp changes.
- Ways artificial viscosity, artificial compression, and hybrid schemes sharpen or stabilize solutions.
- Comparative results showing resolution, speed, and the trade-offs of each approach.
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