Simulation of compressible flows became a routine activity with the appearance of shock-
/contact-capturing methods. These methods can determine all waves, particularly …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

The diffuse interface models, part of the family of the front capturing methods, provide an
efficient and robust framework for the simulation of multi-species flows. They allow the …

This work is devoted to the theory and approximation of nonlinear hyper bolic systems of
conservation laws in one or two space variables. It follows directly a previous publication on …

After the introduction and a review of ODE theory, Chapter 3 develops the main concepts
and properties of nonlinear control systems. In particular, we discuss the relationship …

This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the
Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would …

The goal of this paper is to provide a theoretical framework allowing one to extend some
general concepts related to the numerical approximation of 1-d conservation laws to the …

This paper attempts to give a qualitative and quantitative description of the numerical error
introduced by using finite difference schemes in nonconservative form for scalar …

In some previous works, the authors have introduced a strategy to develop well-balanced
high-order numerical methods for nonconservative hyperbolic systems in the framework of …

This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …