High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

Castro, Manuel J.; Fernández-Nieto, Enrique D.; Ferreiro, A.; Garcia-Rodriguez, Jose; Parés, Carlos

doi:10.1007/s10915-008-9250-4

Cited by 94 publications

(79 citation statements)

References 27 publications

(32 reference statements)

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“…In Figure 5 we compare the numerical and the reference solutions for the free surface level and the first component of the discharge q 1 at times t = 0.05, t = 0.1 and t = 0.15 s, in the longitudinal section y = 1. These results agree with those in [10] and [17].…”

Section: Circular Dam-break Problemsupporting

confidence: 92%

“…We consider a test problem described in [10] and [17]. The domain is the square [0, 2] × [0, 2] and the bottom topography is given by the function:…”

Section: Circular Dam-break Problemmentioning

confidence: 99%

“…In [9], a high-order well-balanced finite volume upwind scheme was developed within a general nonconservative framework. It is a challenge to obtain schemes that compute solutions with high-order accuracy (both in space and time) in the regions where they are smooth, while at the same time shock discontinuities are properly captured (see [10]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

Capilla

Balaguer-Beser

2013

Journal of Computational and Applied Mathematics

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This paper is concerned with the development of high-order well-balanced central schemes to solve the shallow water equations in two spatial dimensions. A Runge-Kutta scheme with a natural continuous extension is applied for time discretization. A Gaussian quadrature rule is used to evaluate time integrals and a three-degree polynomial which calculates point-values from cell averages or flux values by avoiding the increase in the number of solution extrema at the interior of each cell is used as reconstruction operator. That polynomial also guarantees that the number of extrema does not exceed the initial number of extrema and thus it avoids spurious numerical oscillations in the computed solution. A new procedure has been defined to evaluate the flux integrals and to approach the 2D source term integrals in order to verify the exact C-property, using the water surface elevation instead of the water depth as a variable. Numerical experiments have confirmed the high-resolution properties of our numerical scheme in 2D test problems. The well-balanced property of the resulting scheme has also been investigated.

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Section: Circular Dam-break Problemsupporting

confidence: 92%

“…We consider a test problem described in [10] and [17]. The domain is the square [0, 2] × [0, 2] and the bottom topography is given by the function:…”

Section: Circular Dam-break Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

Capilla

Balaguer-Beser

2013

Journal of Computational and Applied Mathematics

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“…We used a first order numerical scheme combined with relatively dense mesh; if more accurate results are required or wider mesh is preferred, the numerical scheme can easily be extended to higher order schemes, as for example in Castro et al (2009a) or Castro et al (2009b). When the interfacial friction factor is chosen appropriately, the model can be used to examine the complex dynamic processes occurring in realistic salt-wedge estuaries, such as Rječina Estuary.…”

Section: Discussionmentioning

confidence: 99%

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

Krvavica

Kožar

Travaš

et al. 2016

Journal of Hydrology and Hydromechanics

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A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Qscheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor was chosen correctly, the agreement between numerical results and field observations was satisfactory.

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“…In particular Tsunami-HySEA implements a PVM-type (polynomial viscosity matrix) method that uses the fastest and the slowest wave speeds, similar to HLL (Harten-Lax-van Leer) method (see . A general overview of the derivation of the high-order methods is shown by Castro et al 2009. For large computational domains and in the framework of Tsunami Early Warning Systems, Tsunami-HySEA also implements a twostep scheme similar to leap-frog for the deep-water propagation step and a second-order TVD-weighted averaged flux (WAF) flux-limiter scheme, described by de la , for close to coast propagation/inundation step.…”

Section: Numerical Solution Methodsmentioning

confidence: 99%

Performance Benchmarking of Tsunami-HySEA Model for NTHMP’s Inundation Mapping Activities

Macías

Castro

Ortega

et al. 2017

Pure Appl. Geophys.

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Abstract-The Tsunami-HySEA model is used to perform some of the numerical benchmark problems proposed and documented in the ''Proceedings and results of the 2011 NTHMP Model Benchmarking Workshop''. The final aim is to obtain the approval for Tsunami-HySEA to be used in projects funded by the National Tsunami Hazard Mitigation Program (NTHMP). Therefore, this work contains the numerical results and comparisons for the five benchmark problems (1, 4, 6, 7, and 9) required for such aim. This set of benchmarks considers analytical, laboratory, and field data test cases. In particular, the analytical solution of a solitary wave runup on a simple beach, and its laboratory counterpart, two more laboratory tests: the runup of a solitary wave on a conically shaped island and the runup onto a complex 3D beach (Monai Valley) and, finally, a field data benchmark based on data from the 1993 Hokkaido Nansei-Oki tsunami.

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High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

Cited by 94 publications

References 27 publications

A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

Performance Benchmarking of Tsunami-HySEA Model for NTHMP’s Inundation Mapping Activities

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