Sensitivity Computations Using Perturbative Methods For Shallow Water Equations

Abstract

We applied the perturbative theory to perform sensitivity analysis of the shallow
water equations. The numerical solution of these equations was found via the mass
lumping finite element technique. Then, the adjoint system of the shallow water equations
was derived for the one-dimensional case and the expression of the sensitivity coefficient
of a generic functional with respect to a generic parameter (Chézy resistance coefficient,
solitary wave amplitude and bed channel slope) was obtained, using the differential
formalism. The sensitivity of the mean functional, representing the first approximation of
the velocity and the depth, was analyzed with regard to these parameters. Results of the
sensitivity coefficients obtained via the perturbative methodology satisfactorily matched
the values computed by the direct method, i.e., by means of the direct solution of the
shallow water equations changing the values of input parameters for each considered
case.