Analysis and numerics for conservation laws

Autori

• Gerald Warnecke

Parametri

• Matematica

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What do a supernova explosion in outer space, flow around an airfoil, and knocking in combustion engines have in common? Despite differences in their physical and chemical mechanisms and scales, they share a common thread: the underlying fluid flows can often be described by similar hyperbolic systems of partial differential equations known as conservation laws. Astrophysicists study supernovae, which are thermo-nuclear explosions on a scale of 10 cm, to gain insights into the universe's fundamental properties. In contrast, engineers analyze flows around airfoils of commercial airliners at a scale of 3 x 10 cm, where shock waves affect wing stability and fuel efficiency. Meanwhile, knocking in combustion engines, occurring at a scale of 10 cm, must be minimized to prevent motor damage and optimize performance for efficiency and environmental concerns. This intersection of interests among astrophysicists, engineers, and mathematicians drives scientific progress in theory and computational methods for solving these equations. The analysis and numerical approximation of solutions to partial differential equations represent a significant area of research in mathematics, with hyperbolic conservation laws in multiple dimensions remaining one of the major challenges in modern mathematics.

Lingua: Inglese

Pubblicato: 2005