The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems

Castro, Manuel J.; Ferreiro, A.; Garcia-Rodriguez, Jose; González‐Vida, J. M.; Macías, Jorge; Parés, Carlos; Vázquez-Cendón, M. Elena

doi:10.1016/j.mcm.2004.01.016

Cited by 116 publications

(132 citation statements)

References 11 publications

Supporting

Mentioning

129

Contrasting

Unclassified

Order By: Relevance

“…In Subsections 5.1 and 5.2 we recall the formulation of these systems as well as the Roe linearizations considered here to derive the different numerical schemes. In order to avoid the appearance of negative values of the thickness of the water layers when wet/dry fronts are present, the corrections proposed in [5] have been applied.…”

Section: Numerical Testsmentioning

confidence: 99%

On some fast well-balanced first order solvers for nonconservative systems

Castro¹,

Pardo²,

Parés³

et al. 2009

Math. Comp.

View full text Add to dashboard Cite

Abstract. The goal of this article is to design robust and simple first order explicit solvers for one-dimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the development of these solvers is the general definition of a Roe linearization introduced by Toumi in 1992 based on the use of a family of paths. Using this concept, Roe methods can be extended to nonconservative systems. These methods have good wellbalanced and robustness properties, but they have also some drawbacks: in particular, their implementation requires the explicit knowledge of the eigenstructure of the intermediate matrices. Our goal here is to design numerical methods based on a Roe linearization which overcome this drawback. The idea is to split the Roe matrices into two parts which are used to calculate the contributions at the cells to the right and to the left, respectively. This strategy is used to generate two different one-parameter families of schemes which contain, as particular cases, some generalizations to nonconservative systems of the well-known Lax-Friedrichs, Lax-Wendroff, FORCE, and GFORCE schemes. Some numerical experiments are presented to compare the behaviors of the schemes introduced here with Roe methods.

show abstract

Section: Numerical Testsmentioning

confidence: 99%

On some fast well-balanced first order solvers for nonconservative systems

Castro¹,

Pardo²,

Parés³

et al. 2009

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…At the same time, this numerical scheme reduces computational times compared with other numerical schemes, while the amplitude of the first tsunami wave is preserved. Concerning the wet-dry fronts discretization, Tsunami-HySEA implements the numerical treatment described by Castro et al (2005) and Gallardo et al (2007) that consists of locally replacing the 1D Riemann solver used during the propagation step, by another 1D Riemann solver that takes into account Water level profiles during runup of the non-breaking wave in the case H/d = 0.019 on the 1:19.85 beach (at times t = 35 (d/g) 1/2 , t = 40 (d/ g) 1/2 , t = 45 (d/g) 1/2 , and t = 50 (d/g) 1/2 . Normalized root mean square deviation (NRMSD) and maximum wave amplitude error (ERR) are computed and shown for each time the presence of a dry cell.…”

Section: Numerical Solution Methodsmentioning

confidence: 99%

“…It has been thoroughly tested, and in particular has passed not only all tests by Synolakis et al (2008), but also other laboratory tests and proposed benchmark problems. Some of them can be found in the studies by Castro et al (2005Castro et al ( , 2006, Gallardo et al (2007), de la , and NTHMP (2016).…”

Section: The Tsunami-hysea Modelmentioning

confidence: 98%

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

Macías

Castro

Ortega

et al. 2017

Pure Appl. Geophys.

View full text Add to dashboard Cite

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.

show abstract

“…We will now describe this adaptation inspired by the work [11] and here extended to the situation where the material can be fluid or plastic.…”

Section: Ii) Wet/dry Frontsmentioning

confidence: 99%

“…Indeed, they may produce nonphysical negative values of the thickness of the water layer near the wet/dry front. Some ways to modify Roe's method to fix these problems have been proposed in [11,10].…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Fernández-Nieto

Gallardo

Vigneaux

2018

Journal of Computational Physics

View full text Add to dashboard Cite

This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of wellbalancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

show abstract

The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems

Cited by 116 publications

References 11 publications

On some fast well-balanced first order solvers for nonconservative systems

On some fast well-balanced first order solvers for nonconservative systems

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

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Contact Info

Product

Resources

About