000079544 001__ 79544
000079544 005__ 20200117211602.0
000079544 0247_ $$2doi$$a10.1016/j.jcp.2018.06.039
000079544 0248_ $$2sideral$$a107032
000079544 037__ $$aART-2018-107032
000079544 041__ $$aeng
000079544 100__ $$0(orcid)0000-0002-3465-6898$$aNavas-Montilla, A.$$uUniversidad de Zaragoza
000079544 245__ $$a2D well-balanced augmented ADER schemes for the Shallow Water Equations with bed elevation and extension to the rotating frame
000079544 260__ $$c2018
000079544 5060_ $$aAccess copy available to the general public$$fUnrestricted
000079544 5203_ $$aIn this work, an arbitrary order augmented WENO-ADER scheme for the resolution of the 2D Shallow Water Equations (SWE) with geometric source term is presented and its application to other shallow water models involving non-geometric sources is explored. This scheme is based in the 1D Augmented Roe Linearized-ADER (ARL-ADER) scheme, presented by the authors in a previous work and motivated by a suitable compromise between accuracy and computational cost. It can be regarded as an arbitrary order version of the Augmented Roe solver, which accounts for the contribution of continuous and discontinuous geometric source terms at cell interfaces in the resolution of the Derivative Riemann Problem (DRP). The main novelty of this work is the extension of the ARL-ADER scheme to 2 dimensions, which involves the design of a particular procedure for the integration of the source term with arbitrary order that ensures an exact balance between flux fluctuations and sources. This procedure makes the scheme preserve equilibrium solutions with machine precision and capture the transient waves accurately. The scheme is applied to the SWE with bed variation and is extended to handle non-geometric source terms such as the Coriolis source term. When considering the SWE with bed variation and Coriolis, the most relevant equilibrium states are the still water at rest and the geostrophic equilibrium. The traditional well-balanced property is extended to satisfy the geostrophic equilibrium. This is achieved by means of a geometric reinterpretation of the Coriolis source term. By doing this, the formulation of the source terms is unified leading to a single geometric source regarded as an apparent topography. The numerical scheme is tested for a broad variety of situations, including some cases where the first order scheme ruins the solution.
000079544 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/CGL2015-66114-R
000079544 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000079544 590__ $$a2.845$$b2018
000079544 591__ $$aPHYSICS, MATHEMATICAL$$b4 / 55 = 0.073$$c2018$$dQ1$$eT1
000079544 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b39 / 106 = 0.368$$c2018$$dQ2$$eT2
000079544 592__ $$a1.643$$b2018
000079544 593__ $$aPhysics and Astronomy (miscellaneous)$$c2018$$dQ1
000079544 593__ $$aComputer Science Applications$$c2018$$dQ1
000079544 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000079544 700__ $$0(orcid)0000-0002-1386-5543$$aMurillo, J.$$uUniversidad de Zaragoza
000079544 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000079544 773__ $$g372 (2018), 316-348$$pJ. comput. phys.$$tJOURNAL OF COMPUTATIONAL PHYSICS$$x0021-9991
000079544 8564_ $$s877479$$uhttps://zaguan.unizar.es/record/79544/files/texto_completo.pdf$$yPostprint
000079544 8564_ $$s112333$$uhttps://zaguan.unizar.es/record/79544/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000079544 909CO $$ooai:zaguan.unizar.es:79544$$particulos$$pdriver
000079544 951__ $$a2020-01-17-21:13:12
000079544 980__ $$aARTICLE