An incomplete LU-based family of preconditioners for numerical resolution of a shallow water system using a duality method—applications Original Research Article

In this paper, we present a family of preconditioners well adapted to the solution of linear problems that arise from a particular discretisation of shallow water equations in the flux form. The formulation of the shallow water equations used here is discretised in time using the method of characteristics and the Euler implicit method, and solved by a duality technique with automatic choice of parameters. The space discretisation is performed using the first-order Raviart-Thomas finite element. The family of preconditioners designed for solving the linear problems that appear at each time iteration greatly improves convergence and significantly reduces the CPU time needed to solve them.