High order schemes for hyperbolic balance laws - Topic 1

Overview

Abstract

Construction of high order finite volume and finite difference shock-capturing schemes for conservation laws.

Topic 1 - illustrating how to construct shock-capturing schemes for conservation laws. We focus on semi-discrete schemes based on the method of lines, which are based on three main ingredients:

• a. the numerical flux function,
• b. high order non-linear reconstruction,
• c. strongly stability preserving schemes for time discretization. Several applications will be given illustrating the accuracy and shock-capturing capability of the schemes.

Brief Biography

Current position: Full Professor of Numerical Analysis Department of Mathematics and Computer Science, University of Catania, Italy

Research interests

Prof. Russo worked on a broad range of topics, giving original contributions in:

1. Experimental and theoretical study of laser annealing induced by laser pulses
2. Asymptotic methods in wave propagation
3. Particle methods
4. Computational fluid dynamics
5. Hydrodynamical models of semiconductors
6. Numerical methods for balance laws
7. Modeling and numerics of kinetic equations
8. Mathematical modeling and simulation of crystal growth
9. Semiclassical limit of the Schroedinger equation
10. Complex networks

His main current research interests concern finite-difference ghost point methods on Cartesian grids, high order semi-implicit schemes for hyperbolic systems with relaxation, asymptotic-preserving schemes in gas dynamics and kinetic theory, numerical methods for highly oscillatory solutions, numerical modeling of sorption kinetics

Scientific production G.Russo has more than one hundred scientific publications in international journals on various topics in applied and computational mathematics and some books.

Bibliographic indices

• Google Scholar as of June 18, 2020
• All: 7917, since 2016: 3631
• H Index 48
• Scopus H-index: 32 with 123 documents
• Total Scopus citations: 3748 by 2603 documents
• Number of co-authors: 129

Professional experience

• 2000-present Full Professor of Numerical Analysis, University of Catania, Italy;
• 1992-2000 Associate Professor of Numerical Analysis, University of L'Aquila, Italy.
• 1990-1992 Research position at the University of L'Aquila, Italy.
• 1987-1990 Postdoctoral position at the Courant Institute of Mathematical Sciences.
• 1982-1983 Research experience for one year on solid-state physics, Physics Institute of the University of Catania.

Educational background

• 1984-1986 Ph.D. in Physics, University of Catania, Italy
• 1976-1982 Laurea degree in Nuclear Engineering, Magna cum Laude, Politecnico di Milano, Italy