Modeling of shock waves in complicated media

We will be considering many aspects of wave propagation in complicated media, such as mixtures of air and water.  For problems with strong shock waves, we will be developing continuum models that respect Newton's laws of motion and thermodynamics of non-ideal materials.  Especially important will be the thermodynamics of mixtures of air and water.  Questions exist as to various forms of these models, especially if they satisfy the second law of thermodynamics.  This relates to the stability properties of the model, which need to be studied. When the model's fundamental stability is established, we will use an existing modern code to simulate shock waves.  The code will use wavelets as basis functions which have useful convergence properties that enables fast and accurate simulation of realistic physics.