5 papers
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…