### 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.

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.

#### Full Text:

PDF

Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**