Space–time SUPG formulation of the shallow‐water equations

Takase, Shinsuke; Kashiyama, Kazuo; Tanaka, Seizo; Tezduyar, Tayfun E.

doi:10.1002/fld.2464

Cited by 38 publications

(41 citation statements)

References 41 publications

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“…It is a uniform mesh, with an element size of 0.2 m in x 1 direction. The computed results are compared with the theoretical results [143] and the results obtained with the Eulerian method [121] based on the semi-discrete SUPG formulation [132] where the semi-discrete equations are solved with the central-difference (Crank-Nicolson) time-integration. With the Eulerian method, we use a coarse mesh with en element size of 0.2 m, and a fine mesh with an element size of 0.1 m. Figure 8 shows the water elevations at the highest and lowest stages of the runup and rundown.…”

Section: Wave Runup Over a Surface With Flat Cross Sectionmentioning

confidence: 99%

“…The shock-capturing parameter is similar to a compressible-flow shock-capturing parameter that was defined in [32,108] in a style that the DCDD [23,32,133] parameter was defined. The computations reported in [132] show that the new shock-capturing parameter has good stability and accuracy properties and the space-time SUPG formulation has better stability and accuracy performance compared to the semi-discrete SUPG formulation where the system of semi-discrete equations is solved with the centraldifference (Crank-Nicolson) time-integration.…”

Section: Introductionmentioning

confidence: 95%

“…It is an effective mathematical model for practical computer simulation of floods, including those caused by tsunamis and storm surges. A good number of numerical methods based on the finite element method have been reported for the SWE (see, for example, [18,[117][118][119][120][121][122][123][124][125][126][127][128][129][130][131][132]). …”

Section: Introductionmentioning

confidence: 99%

“…The stabilization was still (SU PG) 82 with τ 82-MOD and δ 91 . The space-time SUPG formulation of the SWE presented in [132] is also based on the DSD/SST method and included the stabilization parameter τ 04 [32,108] and a new shock-capturing parameter. The shock-capturing parameter is similar to a compressible-flow shock-capturing parameter that was defined in [32,108] in a style that the DCDD [23,32,133] parameter was defined.…”

Section: Introductionmentioning

confidence: 99%

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Space–time SUPG finite element computation of shallow-water flows with moving shorelines

Takase¹,

Kashiyama

Tanaka

et al. 2011

Comput Mech

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We show that combination of the DeformingSpatial-Domain/Stabilized Space-Time and the StreamlineUpwind/Petrov-Galerkin formulations can be used quite effectively for computation of shallow-water flows with moving shorelines. The combined formulation is supplemented with a stabilization parameter that was originally introduced for compressible flows, a compressible-flow shock-capturing parameter adapted for shallow-water flows, and remeshing based on using a background mesh. We present a number of test computations and provide comparisons to theoretical results, experimental data and results computed with nonmoving meshes.

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Section: Wave Runup Over a Surface With Flat Cross Sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

Takase¹,

Kashiyama

Tanaka

et al. 2011

Comput Mech

Self Cite

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“…We implement the proposed approach for boundary conditions in the context of a stabilized finite element formulation, which takes inspiration specifically from [46,50,47] and more broadly from [15,16,51,26,22,27,28,25,24,23,29,49,40]. The proposed embedded method is not limited in applicability, however, to the specific stabilized method considered here.…”

Section: Introductionmentioning

confidence: 99%

The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

Song

Main

Scovazzi

et al. 2018

Journal of Computational Physics

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We propose a new computational approach for embedded boundary simulations of hyperbolic systems. Applications are shown for the linear wave equations and for the nonlinear shallow water system. The proposed approach belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary. Accordingly, boundary conditions, enforced weakly, are appropriately modified to preserve optimal error convergence rates. This framework is applied here in the setting of a stabilized finite element method, even though other spatial discretization techniques could have been employed. Accuracy, stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations. Comparisons with standard weak boundary conditions imposed on grids that conform to the geometry of the computational domain boundaries are also presented. § Team CARDAMOM, INRIA Bordeaux Sud-Ouest, 200 av. de la vieille tour33405 Talence Cedex, France Shifted boundary method pour systèmes hyperboliques:ondes linéaires et équations shallow waterRésumé : On propose une nouvelle approche pour des simulations avec bords immergés pour des systèmes hyperboliques et en particulier les équations shallow water. L'approche proposée consiste en modifier les conditions au bords avec un développement limité permettant d'assurer l'ordre deux avec des embedded boundaries. L'approche est implementé est validée ici dans le cadre d'une méthode de type stabilized finite element sur un très grand nombre de cas tests représentatifs d'applications de propagation de vagues et inondation.

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Fluid–Structure Interaction and Flows with Moving Boundaries and Interfaces

Tezduyar

Takizawa

Bazilevs

2017

Encyclopedia of Computational Mechanics Second Edition

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Flows with moving boundaries and interfaces (MBI) include fluid–structure interaction and a number of other classes of problems, such as fluid–object interaction, fluid–particle interaction, free‐surface and multifluid flows, and flows with solid surfaces in fast, linear, or rotational relative motion. These problems are frequently encountered in engineering analysis and design, pose some of the most formidable computational challenges, and have a common core computational technology need. Bringing solution and analysis to them motivated the development of a good number of core computational methods and special methods targeting specific classes of MBI problems. This chapter is an overview of some of those core and special methods, with a focus on computational examples from the ST‐VMS and ALE‐VMS methods and special methods developed in conjunction with the two.

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Space–time SUPG formulation of the shallow‐water equations

Cited by 38 publications

References 41 publications

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

Fluid–Structure Interaction and Flows with Moving Boundaries and Interfaces

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