An Algorithm for Source Reconstruction in Nonlinear Shallow-Water Equations

• Published in: Computational mathematics and mathematical physics Vol. 58; no. 8; pp. 1334 - 1343
• Main Authors: Kabanikhin, S. I., Krivorotko, O. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.08.2018; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Computer simulation; Finite volume method; Inverse problems; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear equations; Numerical analysis; Reconstruction; Shallow water equations; inverse problem; optimization; source reconstruction; regularization; conjugate gradient method; finite volume method; nonlinear shallow-water equations; gradient of objective functional
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542518080109

A numerical algorithm is proposed to solve the source reconstruction problem for a system of nonlinear shallow-water equations using the dynamics of water surface perturbation measured at a finite number of spatial points and/or over a part of the surface at a fixed time. The combined inverse problem under study is reduced to the minimization of an objective functional characterizing the quadratic deviation of simulated data from measured data (a misfit function). An explicit expression for the gradient of the misfit function is obtained. The direct and conjugate problems within the framework of shallow-water equations are solved by the finite volume method. The numerical results are analyzed and compared with experimental data.