Albi G. Advances in Numerical Methods for Hyperbolic Balance Laws..Problems 2023

Textbook in PDF format

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.
Preface
Contributors
A Tree Structure Approach to Reachability Analysis
Asymptotic-Preserving Neural Networks for Hyperbolic Systems with Diffusive Scaling
A Non-local System Modeling Bi-directional Traffic Flows
Semi-implicit Finite-Difference Methods for Compressible Gas Dynamics with Curved Boundaries: A Ghost-Point Approach
High-Order Arbitrary-Lagrangian-Eulerian Schemes on Crazy Moving Voronoi Meshes
Overview on Uncertainty Quantification in Traffic Models via Intrusive Method
A Study of Multiscale Kinetic Models with Uncertainties
On the Shock Wave Discontinuities in Grad Hierarchy for a Binary Mixture of Inert Gases
A Conservative a-Posteriori Time-Limiting Procedure in Quinpi Schemes
Applications of Fokker Planck Equations in Machine Learning Algorithms