Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flow

Carole Delenne (1) , Pascal Finaud-Guyot (1, 2) , Vincent Guinot (1) , Bernard Cappelaere (1)

1 HSM - Hydrosciences Montpellier
2 IMFS - Institut de Mécanique des Fluides et des Solides

A finite volume-based numerical technique is presented concerning the sensitivity of the solution of the one-dimensional Shallow Water Equations (SWEs) with scalar transport. An approximate Riemann solver is proposed for direct sensitivity calculation even in the presence of discontinuous solutions. The ShallowWater Sensitivity Equations (SWSEs) are first derived as well as the expressions of the sensitivity source terms, initial and boundary conditions. The numerical technique is then detailed and application examples are provided to assess the method's efficiency in estimating the sensitivity to different parameters (friction coefficient and initial and boundary conditions). The application of the dam-break problem to a trapezoidal channel is also provided. The comparison with the analytical solution and the classical empirical approach illustrates the usefulness of the direct sensitivity calculation.

Mots clés: shallow water equations; sensitivity; finite volume; Riemann solver; source terms; initial and boundary conditions

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Modélisation et simulation

Carole Delenne, Pascal Finaud-Guyot, Vincent Guinot, Bernard Cappelaere. Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flow. International Journal for Numerical Methods in Fluids, 2010, pp.10.1002/fld.2398. ⟨10.1002/fld.2398⟩. ⟨hal-00515826⟩