Comptes Rendus
Direct sensitivity computation for the Saint-Venant equations with hydraulic jumps
Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 766-771.

This Note presents a new Riemann solver for the Saint-Venant equations in conjunction with the sensitivity problem when the solutions are discontinuous. The solver is based on the a priori assumption of two rarefaction waves. The presence of shocks is detected a posteriori and an extra sensitivity term in the form of a Dirac source term is accounted for in the sensitivity balance equations.

On propose ici un solveur de Riemann pour résoudre les équations de sensibilité conjointement à la projection sur une dimension des équations de Saint-Venant dans le cas de solutions discontinues. Le solveur est basé sur la supposition a priori de deux ondes de raréfaction. La présence de chocs est détectée a posteriori et un terme supplémentaire, sous la forme d'un terme source de Dirac, est introduit dans l'équilibre des équations de sensibilité.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2008.09.006
Keywords: Computational fluid mechanics, Sensitivity, Hyperbolic conservation laws, Shocks
Mot clés : Mécanique des fluides numérique, Sensibilités, Lois de conservation hyperboliques, Chocs

Carole Delenne 1; Vincent Guinot 1; Bernard Cappelaere 1

1 Hydrosciences Montpellier, UMR 5569, Université Montpellier 2, place Eugène Bataillon (CCMSE), 34095 Montpellier Cedex 5, France
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Carole Delenne; Vincent Guinot; Bernard Cappelaere. Direct sensitivity computation for the Saint-Venant equations with hydraulic jumps. Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 766-771. doi : 10.1016/j.crme.2008.09.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.09.006/

[1] M.D. Gunzburger Sensitivities, adjoints and flow optimization, Int. J. Numer. Methods Fluids, Volume 31 (1999), pp. 53-78

[2] C. Bardos; O. Pironneau A formalism for the differentiation of conservation laws, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 839-845

[3] V. Guinot; M. Leménager; B. Cappelaere Sensitivity equations for hyperbolic conservation law-based flow models, Adv. Water Resour., Volume 30 (2007), pp. 1943-1961

[4] P.D. Lax Hyperbolic systems of conservation laws, Comm. Pure Appl. Math., Volume 10 (1957), pp. 537-566

[5] E.F. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1997

[6] V. Guinot Godunov-type Schemes. An Introduction for Engineers, Elsevier, 2003

[7] V. Guinot Riemann solvers for water hammer simulations by Godunov method, Int. J. Numer. Methods Engrg., Volume 49 (2000), pp. 851-870

[8] J. Lhomme; V. Guinot A general, approximate-state Riemann solver for hyperbolic systems of conservation laws with source terms, Int. J. Numer. Methods Fluids, Volume 56 (2007), pp. 1605-1623

[9] V. Guinot Ondes en mécanique des fluides. Modélisation et simulation numérique, Hermes Publishing, 2006 (in French)

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