The Numerical Solution of Data Assimilation Problem for Shallow Water Equations

The problem on propagation of long waves in a domain of arbitrary form with the sufficiently smooth boundary on a sphere is considered. The boundary consists of ”solid” parts passing along the coastline and ”liquid” parts passing through the water area. We assume, free surface level observation data on ”liquid” boundary is known. In general case the boundary condition on ”liquid” part of boundary contains unknown boundary function, which must be found together with component of velocity vector and free surface level. We put an assimilation observation data problem by Prof. V.I. Agoshkov methodology. To solve our ill-posed inverse problem an approach, based on optimal control methods and adjoint equations theory, is used. Numerical solution of direct and adjoint problems is based on finite elements method. Parallel software using MPI is discussed.