Adaptive multiscale scheme based on numerical density of entropy production for conservation laws

Ersoy, Mehmet; Golay, Frédéric; Yushchenko, Lyudmyla

doi:10.2478/s11533-013-0252-6

Cited by 14 publications

(45 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To increase the accuracy, second order space and time integration can be used, see for instance ERSOY et al (2013) andMARCHE (2005). For the source term treatment, the hydrostatic reconstruction of AUDUSSE et al (2004) is used allowing a well-balanced scheme.…”

Section: Finite Volume Methods On Unstructured Meshmentioning

confidence: 99%

“…Another parameter possibly affecting the propagation is the lack of accuracy about the bathymetry resolution close to the shore. To finish, due to large bathymetry variations, the non-hydrostatic effects may have consequences on the wave propagation as shown by DUTYKH & CLAMOND (2015) on an academic test case.…”

Section: Figure 5 Comparisons Of Uniform and Amr Simulations With Gpmentioning

confidence: 99%

See 1 more Smart Citation

The Saint-Venant model for tsunami propagation simulation: Application to the 2011 Tohoku event

Pons¹,

Marcer²,

Golay³

2016

XIVèmes Journées, Toulon

Self Cite

View full text Add to dashboard Cite

Abstract:Beside a validation step of numerical models regarding academic tsunami test cases, one of the topic of the TANDEM project aims to qualify long distance propagation models on real tsunami events. In this context, the Saint-Venant model is used to simulate the 2011 Tohoku tsunami in Japan. The numerical resolution is based on a well-balanced finite volumes solver on unstructured mesh. The results are compared to available near and far shore in-situ data. The numerical accuracy is improved by the use of an adaptive mesh refinement method. The relevancy of a non-dispersive model for this event is then discussed.

show abstract

Section: Finite Volume Methods On Unstructured Meshmentioning

confidence: 99%

Section: Figure 5 Comparisons Of Uniform and Amr Simulations With Gpmentioning

confidence: 99%

The Saint-Venant model for tsunami propagation simulation: Application to the 2011 Tohoku event

Pons¹,

Marcer²,

Golay³

2016

XIVèmes Journées, Toulon

Self Cite

View full text Add to dashboard Cite

show abstract

“…Locally, the mesh is coarser or finer according to the value of its numerical production of entropy relative to the numerical production of entropy of the whole domain. More details can be found in [6]. As the choice of this threshold value is important, an improvement has been recently done in order to determine automatically this value [11].…”

Section: Block Based Adaptive Mesh Refinement Procedures (Bb-amr)mentioning

confidence: 99%

“…When dispersive effects are important, the Boussinesq or the Green Naghdi model are well adapted, but generally a quite simple model as the Saint-Venant model is used [7,10]. It leads to an hyperbolic system of equations, where the numerical production of entropy can be used as mesh refinement indicator [6,1]. One of the difficulty of AMR method is the projection step where the variable are defined from an old mesh to a new one.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Mesh Refinement Method Applied to Shallow Water Model: A Mass Conservative Projection

Pons¹,

Golay²,

Marcer³

2017

Topical Problems of Fluid Mechanics 2017

View full text Add to dashboard Cite

In the tsunami waves context, efficient numerical methods are necessary to simulate multi scales events. One way to reduce the computational cost is to use an adaptive mesh refinement method on unstructured meshes. This approach is used in this paper with a finite volume scheme solving the multi-dimensional Saint-Venant system. The adaptive mesh refinement method follows a block-based decomposition (called BB-AMR), which allows quick meshing and easy parallelization. One step of the AMR method is the so-called projection step where the new mesh values have to be defined from the old ones. For vertically integrated model the bathymetry variation during the projection step plays a crucial role on the mass conservation. To avoid large deficit or excess of mass a special attention is given to the projection step. Finally a 3D test case simulation is compared to experimental results to illustrated the quasi conservation of the mass with an appropriated projection method.

show abstract

“…This property makes the NEP able to detect the smoothness of solutions to the SWE. NEP has been successfully implemented in gas dynamics and other conservation laws by a number of authors, such as Ersoy et al [2], Golay [3] and Puppo [12,13]. NEP can also be used to investigate the accuracy of numerical methods [14].…”

Section: Introductionmentioning

confidence: 99%

Numerical Entropy Production of the One-and-a-Half-Dimensional Shallow Water Equations With Topography

Mungkasi

2015

JIMS

View full text Add to dashboard Cite

Abstract. Numerical entropy production can be used as a smoothness indicator of solutions to conservation laws. By definition the entropy production is non-positive. However some authors, using a finite volume method framework, showed that positive overshoots of the numerical entropy production were possible for conservation laws (no source terms involved). Note that the one-and-a-half-dimensional shallow water equations without source terms are conservation laws. A report has been published regarding the behaviour of the numerical entropy production of the oneand-a-half-dimensional shallow water equations without source terms. The main result of that report was that positive overshoots of the numerical entropy production were avoided by use of a modified entropy flux which satisfies a discrete numerical entropy inequality. In the present article we consider an extension problem of the previous report. We take the one-and-a-half-dimensional shallow water equations involving topography. The topography is a source term in the considered system of equations. Our results confirm that a modified entropy flux which satisfies a discrete numerical entropy inequality is indeed required to have no positive overshoots of the entropy production.Key words and Phrases: Numerical entropy production, shallow water equations, smoothness indicator, finite volume method. S. MungkasiAbstrak. Produksi entropi numeris dapat digunakan sebagai indikator kehalusan fungsi penyelesaian hukum-hukum kekekalan. Berdasarkan definisi, produksi entropi adalah tak-positif. Namun demikian, menggunakan suatu kerangka metode volume hingga beberapa peneliti menunjukkan bahwa produksi entropi numeris bisa saja bernilai positif pada titik-titik tertentu untuk hukum-hukum kekekalan (tidak ada suku sumber dalam persamaan yang diselesaikan). Perlu dicatat bahwa persamaan air dangkal satu setengah dimensi yang tidak melibatkan suku sumber merupakan hukum kekekalan. Sebuah laporan tentang perilaku produksi entropi numeris untuk persamaan air dangkal satu setengah dimensi tanpa suku sumber telah diterbitkan. Hasil utama laporan tersebut adalah nilai positif produksi entropi numeris dapat dihindari menggunakan flux entropi termodifikasi yang memenuhi suatu pertidaksamaan entropi numeris diskret. Dalam artikel saat ini, dipandang suatu masalah yang lebih umum, yaitu persamaan air dangkal satu setengah dimensi yang melibatkan topografi. Topografi ini adalah suatu suku sumber dalam sistem persamaan yang dipandang. Hasil dalam artikel ini menegaskan bahwa suatu flux entropi termodifikasi yang memenuhi suatu pertidaksamaan entropi numeris diskret memang sungguh-sungguh diperlukan untuk menghindari timbulnya produksi entropi yang bernilai positif.Kata kunci: Produksi entropi numeris, persamaan air dangkal, indikator kehalusan, metode volume hingga.

show abstract

Adaptive multiscale scheme based on numerical density of entropy production for conservation laws

Cited by 14 publications

References 30 publications

The Saint-Venant model for tsunami propagation simulation: Application to the 2011 Tohoku event

The Saint-Venant model for tsunami propagation simulation: Application to the 2011 Tohoku event

Adaptive Mesh Refinement Method Applied to Shallow Water Model: A Mass Conservative Projection

Numerical Entropy Production of the One-and-a-Half-Dimensional Shallow Water Equations With Topography

Contact Info

Product

Resources

About