This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems.

The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

Focuses on the mathematical interplay between Eulerian and Lagrangian formulations and its significance for numerical methods Explains the structure of modern corner-based Lagrangian solvers Details the linear-quadratic structure of Lagrangian fluxes originating from continuum mechanics

Inhalt
Models.- Conservation laws.- Systems and Lagrangian systems.- Numerical discretization.- Starting from the mesh.