6533b83afe1ef96bd12a7885

RESEARCH PRODUCT

Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function

José M. GallardoManuel J. CastroAntonio Marquina

subject

CouplingPolynomialWork (thermodynamics)Ideal (set theory)MathematicsofComputing_NUMERICALANALYSISEuler equationsRiemann hypothesissymbols.namesakeComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONsymbolsApplied mathematicsMagnetohydrodynamicsShallow water equationsMathematics

description

We give an overview on the work developed in recent years about certain classes of incomplete Riemann solvers for hyperbolic systems. These solvers are based on polynomial or rational approximations to |x|, and they do not require the knowledge of the complete eigenstructure of the system, but only a bound on the maximum wave speed. Our solvers can be readily applied to nonconservative hyperbolic systems, by following the theory of path-conservative schemes. In particular, this allows for an automatic treatment of source or coupling terms in systems of balance laws. The properties of our schemes have been tested with some challenging numerical experiments involving systems such as the Euler equations, ideal magnetohydrodynamics equations and multilayer shallow water equations.

yearjournalcountryeditionlanguage
2021-01-01
https://doi.org/10.1007/978-3-030-72850-2_1