Consider a balance law where the flux may depend explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below, we deduce the evolution in the smooth case from the jump conditions at discontinuities. Moreover, the resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, to the flow of water in a canal with varying width and depth, as well as to the inviscid Euler equations in pipes with varying geometry.

Colombo, R., Guerra, G., Holle, Y. (2024). Balance Laws with Singular Source Term and Applications to Fluid Dynamics. In C. Parés, M.J. Castro, T. Morales de Luna, M.L. Muñoz-Ruiz (a cura di), Hyperbolic Problems: Theory, Numerics, Applications. Volume II HYP2022, Málaga, Spain, June 20-24, 2022 Conference proceedings (pp. 313-323). Springer Nature [10.1007/978-3-031-55264-9_27].

Balance Laws with Singular Source Term and Applications to Fluid Dynamics

Guerra, G.
;
2024

Abstract

Consider a balance law where the flux may depend explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below, we deduce the evolution in the smooth case from the jump conditions at discontinuities. Moreover, the resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, to the flow of water in a canal with varying width and depth, as well as to the inviscid Euler equations in pipes with varying geometry.
Capitolo o saggio
Fluid flows in pipes; Well posedness for balance laws with measure source term
English
Hyperbolic Problems: Theory, Numerics, Applications. Volume II HYP2022, Málaga, Spain, June 20-24, 2022 Conference proceedings
Parés, C; Castro, MJ; Morales de Luna, T; Muñoz-Ruiz, ML
2024
9783031552632
Springer Nature
313
323
Colombo, R., Guerra, G., Holle, Y. (2024). Balance Laws with Singular Source Term and Applications to Fluid Dynamics. In C. Parés, M.J. Castro, T. Morales de Luna, M.L. Muñoz-Ruiz (a cura di), Hyperbolic Problems: Theory, Numerics, Applications. Volume II HYP2022, Málaga, Spain, June 20-24, 2022 Conference proceedings (pp. 313-323). Springer Nature [10.1007/978-3-031-55264-9_27].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/484499
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