Implicit finite volume solution of the bidimensional Shallow Water Equations in unstructured meshes: Application to river flow

Implicit schemes are generally the choice in steady state problems, although in the case of the Shallow Water Equations (SWE) their use has been principally restricted to models based on structured grids. Few references can be found of implicit bidimensional SWE models that solve unsteady problems in unstructured meshes. In this work a novel family of implicit time integration methods is presented, which can be successfully cast in unstructured meshes. The solution procedure relies on a Newton inner iteration whose purpose is to recover the non-linearity of the SWE system every physical time step. An approximate factorization approach has been adopted to overcome the difficulty associated with the solution of large algebraic systems with complex structure. Finally, the application of the method in a real test case involving the propagation of a flood wave along a natural valley is analyzed and the results compared against explicit schemes.