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Finite Volume Methods for Hyperbolic Problems
This book contains an introduction to hyperbolic partial differential equations and a powerful
class of numerical methods for approximating their solution, including both linear
problems and nonlinear conservation laws. These equations describe a wide range of wavepropagation
and transport phenomena arising in nearly every scientific and engineering
discipline. Several applications are described in a self-contained manner, along with much
of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov’s
method are developed, in which Riemann problems are solved to determine the local wave
structure and limiters are then applied to eliminate numerical oscillations. These methods
were originally designed to capture shock waves accurately, but are also useful tools
for studying linear wave-propagation problems, particularly in heterogenous material. The
methods studied are implemented in the CLAWPACK software package. Source code for all
the examples presented can be found on the web, along with animations of many timedependent
solutions. This provides an excellent learning environment for understanding
wave-propagation phenomena and finite volume methods.
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