000076895 001__ 76895
000076895 005__ 20200221144342.0
000076895 0247_ $$2doi$$a10.1016/j.jcp.2016.04.047
000076895 0248_ $$2sideral$$a95011
000076895 037__ $$aART-2016-95011
000076895 041__ $$aeng
000076895 100__ $$0(orcid)0000-0002-3465-6898$$aNavas-Montilla, A.$$uUniversidad de Zaragoza
000076895 245__ $$aAsymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms
000076895 260__ $$c2016
000076895 5060_ $$aAccess copy available to the general public$$fUnrestricted
000076895 5203_ $$aIn this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) 1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the FS solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the FS solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed FS and LFS solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed.
000076895 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000076895 590__ $$a2.744$$b2016
000076895 591__ $$aPHYSICS, MATHEMATICAL$$b3 / 55 = 0.055$$c2016$$dQ1$$eT1
000076895 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b26 / 105 = 0.248$$c2016$$dQ1$$eT1
000076895 592__ $$a2.048$$b2016
000076895 593__ $$aPhysics and Astronomy (miscellaneous)$$c2016$$dQ1
000076895 593__ $$aComputer Science Applications$$c2016$$dQ1
000076895 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion
000076895 700__ $$0(orcid)0000-0002-1386-5543$$aMurillo, J.$$uUniversidad de Zaragoza
000076895 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000076895 773__ $$g317 (2016), 108-147$$pJ. comput. phys.$$tJOURNAL OF COMPUTATIONAL PHYSICS$$x0021-9991
000076895 8564_ $$s1370964$$uhttps://zaguan.unizar.es/record/76895/files/texto_completo.pdf$$yPreprint
000076895 8564_ $$s77454$$uhttps://zaguan.unizar.es/record/76895/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint
000076895 909CO $$ooai:zaguan.unizar.es:76895$$particulos$$pdriver
000076895 951__ $$a2020-02-21-13:50:45
000076895 980__ $$aARTICLE