000070883 001__ 70883
000070883 005__ 20190709135529.0
000070883 0247_ $$2doi$$a10.1016/j.jcp.2017.03.057
000070883 0248_ $$2sideral$$a98559
000070883 037__ $$aART-2017-98559
000070883 041__ $$aeng
000070883 100__ $$0(orcid)0000-0002-3465-6898$$aNavas-Montilla, A.$$uUniversidad de Zaragoza
000070883 245__ $$aOvercoming numerical shockwave anomalies using energy balanced numerical schemes. Application to the Shallow Water Equations with discontinuous topography
000070883 260__ $$c2017
000070883 5060_ $$aAccess copy available to the general public$$fUnrestricted
000070883 5203_ $$aWhen designing a numerical scheme for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced STD based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the STD procedure required should not be merely based on ad hoc approximations. The STD proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the STD must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some numerical anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative STD that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the SWE containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though it does not disturb the rest of the solution in steady cases, when considering transient cases it produces a very undesirable shedding of spurious oscillations downstream that should be circumvented. Based on spike-reducing techniques (originally designed for homogeneous Euler equations) that propose the construction of interpolated fluxes in the untrustworthy regions, we design a novel Roe-type scheme for the SWE with discontinuous topography that reduces the presence of the aforementioned spurious spike. The resulting spike-reducing method in combination with the proposed STD ensures an accurate positioning of steady jumps, provides convergence with mesh refinement, which was not possible for previous methods that cannot avoid the spike.
000070883 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/CGL2015-66114-R
000070883 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000070883 590__ $$a2.864$$b2017
000070883 591__ $$aPHYSICS, MATHEMATICAL$$b3 / 55 = 0.055$$c2017$$dQ1$$eT1
000070883 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b30 / 105 = 0.286$$c2017$$dQ2$$eT1
000070883 592__ $$a2.047$$b2017
000070883 593__ $$aPhysics and Astronomy (miscellaneous)$$c2017$$dQ1
000070883 593__ $$aComputer Science Applications$$c2017$$dQ1
000070883 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000070883 700__ $$0(orcid)0000-0002-1386-5543$$aMurillo, J.$$uUniversidad de Zaragoza
000070883 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000070883 773__ $$g340 (2017), 575-616$$pJ. comput. phys.$$tJOURNAL OF COMPUTATIONAL PHYSICS$$x0021-9991
000070883 8564_ $$s4269208$$uhttps://zaguan.unizar.es/record/70883/files/texto_completo.pdf$$yPostprint
000070883 8564_ $$s75726$$uhttps://zaguan.unizar.es/record/70883/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000070883 909CO $$ooai:zaguan.unizar.es:70883$$particulos$$pdriver
000070883 951__ $$a2019-07-09-12:01:24
000070883 980__ $$aARTICLE