TY - JOUR

T1 - Behaviour of the numerical entropy production of the one-and-a-half- dimensional shallow water equations

AU - Mungkasi, Sudi

AU - Roberts, Stephen G.

PY - 2012

Y1 - 2012

N2 - This article reports the behaviour of the numerical entropy production of the one-and-a-half-dimensional shallow water equations. The one-and-a-half- dimensional shallow water equations are the onedimensional shallow water equations with a passive tracer or transverse velocity. The studied behaviour is with respect to the choice of numerical fluxes to evolve the mass, momentum, tracer-mass (transverse momentum), and entropy. When solving the one-and-a-half-dimensional shallow water equations using a finite volume method, we recommend the use of a double sided stencil flux for the mass and momentum, and in addition, a single sided stencil (upwind) flux for the tracer-mass. Having this recommended combination of fluxes, we use a double sided stencil entropy flux to compute the numerical entropy production, but this flux generates positive overshoots of the numerical entropy production. Positive overshoots of the numerical entropy production are avoided by use of a modified entropy flux, which satisfies a discrete numerical entropy inequality.

AB - This article reports the behaviour of the numerical entropy production of the one-and-a-half-dimensional shallow water equations. The one-and-a-half- dimensional shallow water equations are the onedimensional shallow water equations with a passive tracer or transverse velocity. The studied behaviour is with respect to the choice of numerical fluxes to evolve the mass, momentum, tracer-mass (transverse momentum), and entropy. When solving the one-and-a-half-dimensional shallow water equations using a finite volume method, we recommend the use of a double sided stencil flux for the mass and momentum, and in addition, a single sided stencil (upwind) flux for the tracer-mass. Having this recommended combination of fluxes, we use a double sided stencil entropy flux to compute the numerical entropy production, but this flux generates positive overshoots of the numerical entropy production. Positive overshoots of the numerical entropy production are avoided by use of a modified entropy flux, which satisfies a discrete numerical entropy inequality.

KW - Finite volume methods

KW - Numerical entropy production

KW - Passive tracer

KW - Refinement indicator

KW - Shallow water equations

KW - Smoothness indicator

KW - Transverse velocity

UR - http://www.scopus.com/inward/record.url?scp=84897872177&partnerID=8YFLogxK

M3 - Article

SN - 1446-1811

VL - 54

SP - C18-C33

JO - ANZIAM Journal

JF - ANZIAM Journal

IS - SUPPL

ER -