6 papers
Philip L. Roe, the British Scientist. The Cranfield Years and Beyond
Eleuterio F. Toro
Philip L. Roe, the renowned British scientist, passed away on April 26, 2026, at the age of 87, while Professor Emeritus at the University of Michigan. My association with Phil Roe…
Reminiscences of S. K. Godunov. The Russian Mathematician
Eleuterio F. Toro
These personal reminiscences of the great Russian mathematician Sergey K. Godunov (1929-2023) arose from a request by his daughter, Ekaterina, to contribute a piece to a book she i…
FORCE- Numerical Fluxes within the Arbitrary High Order Semidiscrete WENO-DeC Framework: A Competitive Alternative to Upwind Fluxes
Lorenzo Micalizzi, Eleuterio Toro
This work systematically investigates the performance of FORCE-- numerical fluxes within an arbitrary high order semidiscrete finite volume (FV) framework for hyperbolic partial…
High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics
Shaoshuai Chu, Michael Herty, Eleuterio F. Toro
We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-…
Algorithms of very high space-time orders of accuracy for hyperbolic equations in the semidiscrete WENO-DeC framework
Lorenzo Micalizzi, Eleuterio F. Toro
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis o…
Rusanov-type Schemes for Hyperbolic Equations: Wave-Speed Estimates, Monotonicity and Stability
Eleuterio F. Toro, Svetlana A. Tokareva
HLL-type schemes constitute a large hierarchy of numerical methods, in the finite volume and discontinuous Galerkin finite element frameworks, for solving hyperbolic equations. The…