Summary: JNTERNATIONALJOURNALFOR NUMERICAL METHODS I N FLUIDS,VOL. 20, 157-168 (1995)
APPROXIMATION OF SHALLOW WATER EQUATIONS BY
ROE'S RIEMANN SOLVER
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The inviscid shallow water equations provide a genuinely hyperbolic system and all the numerical tools
that have been developed for a system of conservation laws can be applied to them. However, this system
of equations presents some peculiarities that can be exploited when developing a numerical method based
on Roe's Riemann solver and enhanced by a slope limiting of MUSCL type. In the present paper a TVD
version of the Lax-Wendroff scheme is used and its performance is shown in ID and 2D computations.
Then two specific difficulties that arise in this context are investigated. The former is the capability of this
class of schemes to handle geometric source terms that arise to model the bottom variation. The latter
analysis pertains to situations in which strict hyperbolicity is lost, i.e. when two eigenvalues collapse into
KEY WORDS Shallow water equations Flux difference splitting Open channel flow High resolution schemes
In recent years there has been a great effort devoted to the definition of efficient and accurate
numerical methods for hyperbolic systems and most of all the Euler equations of gas dynamics.
From the mathematical point of view the hyperbolic equations are well known to admit