A domain decomposition method for conservation laws with discontinuous flux function

Herty, Michaël; Seaı̈d, Mohammed; Singh, Anita

doi:10.1016/j.apnum.2006.04.003

Cited by 8 publications

(10 citation statements)

References 23 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, there has been a growth of interest in coupled systems of hyperbolic equations with applications to gas and water networks, see for example [4,8,13,26,14] for theoretical studies and [1,20,21] for numerical discussions. So far, the existing theoretical results treat the one-dimensional situation.…”

Section: Coupling Conditions At the Canal-to-canal Intersectionsmentioning

confidence: 99%

“…It has been proven that under suitable assumptions this procedure gives existence, uniqueness and Lipschitz dependence on the initial data for general 2×2-system of conservation laws and for rather general coupling conditions, we refer the reader to [9] for more details. The results of this discussion can be used in modified Riemann solvers for numerical purposes, see [5,4,1,21] for a situation of two coupled gas pipes with different flux functions. This approach is similar to the solution of initial-boundary value problems for hyperbolic systems with the difference being that in the present case we additionally have to satisfy some algebraic conditions.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Assessment of coupling conditions in water way intersections

Herty

Seaı̈d

2012

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Publisher's copyright statement:his is the epted version of the following rti leX rertyD wF nd e ¤ %dD wF @PHIQAD essessment of oupling onditions in w ter w y interse tionsF sntern tion l tourn l for xumeri l wethods in pluidsD UI @IIAX IRQVEIRTHD whi h h s een pu lished in (n l form t httpXGGdxFdoiForgGIHFIHHPG)dFQUIWF his rti le m y e used for nonE ommer i l purposes in ord n e ith iley erms nd gonditions for selfE r hivingFAdditional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. SUMMARYWe present a numerical assessment of coupling conditions in T-junction for water flow in open canals. The mathematical model is based on the well-established shallow water equations for open channel flows. In the present work, the emphasis is given to the description of coupling conditions at canalto-canal intersections. The accurate prediction of these coupling conditions is essential in order to achieve good performance and reliable numerical simulations of water canals in networks. There is exists several theoretical results for coupling conditions in a reduced geometry. The purpose of our work is to numerically verify these conditions for different water flow regimes. More precisely, we consider a local zooming of the T-junction resulting in a two-dimensional flow problem at the canals intersection. A high-order non-oscillatory method is used for solving the governing two-dimensional equations and the water flow solutions are space-averaged over the junction areas. The obtained numerical results are thereafter, used for verification and comparison with the theoretical results. Verifications are conducted for two types of junctions namely the 1-to-2 and 2-to-1 situations.

show abstract

Section: Coupling Conditions At the Canal-to-canal Intersectionsmentioning

confidence: 99%

mentioning

confidence: 99%

Assessment of coupling conditions in water way intersections

Herty

Seaı̈d

2012

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…We present a construction as in existing literature. A general result for coupling of the same spatially 1D conservation law has been presented, eg, in Colombo et al 35 The coupling of different scalar conservation laws has been discussed also in Herty et al 36 Further references and an application of those techniques to other models can be found, eg, in Bressan et al 28 and, eg, in Godlewski and Raviart, 24,25 Godlewski et al, 26 and Adimurthi and Veerappa. 37 We proceed as follows: First, we recall the notion of half-Riemann problems and admissible boundary values for the trace of a solution to a general system of conservation laws (see also Dubois and Lefloch 38 ).…”

Section: Well-posedness On the Coupling Conditionsmentioning

confidence: 96%

Fluid‐structure coupling of linear elastic model with compressible flow models

Herty

Müller

Gerhard

et al. 2017

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Summary Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.

show abstract

“…On the other hand, scalar conservation laws with discontinuous flux arise from the differentiation of Hamilton-Jacobi equations modelling shape-from-shading problems [18,19]. A thorough understanding of the problem (1.2), (1.3) is at the core of the well-posedness and numerical analysis of models of "network" type, in which the topology of the computational domain consists of a number of one-dimensional edges that are coupled at their endpoints forming "junctions" [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Conservation laws with discontinuous flux: a short introduction

Bürger

Karlsen

2008

J Eng Math

View full text Add to dashboard Cite

Conservation laws with discontinuous flux have attracted recent attention both due to their numerous applications and the intriguing theoretical challenges raised by their well-posedness and numerical analysis. This introductory note states the basic problem considered in the eight contributions of this Special Issue. Three different types of applications are surveyed where these equations appear, motivated by spatially heterogeneous physical models, adjoint problems for parameter identification, and numerical methods for systems of conservation laws, respectively. Basic problems arising in the analysis of these equations are discussed, and the contributions of the Special Issue are presented.

show abstract

A domain decomposition method for conservation laws with discontinuous flux function

Cited by 8 publications

References 23 publications

Assessment of coupling conditions in water way intersections

Assessment of coupling conditions in water way intersections

Fluid‐structure coupling of linear elastic model with compressible flow models

Conservation laws with discontinuous flux: a short introduction

Contact Info

Product

Resources

About