Well balanced high order numerical methods for nonlinear hyperbolic systems. Applications to the simulation of geophysical flows

PI: Manuel J. Castro Díaz
co-PI: Carlos Parés Madroñal

Abstract: The main objective of this project is the development and improvement of numerical models that constitute useful tools in the prediction and management of catastrophes caused by geophysical flows, such as floods, tsunamis or “storm surges”. New models for these problems will be developed that incorporate non-hydrostatic effects, and that can be formulated as nonlinear hyperbolic systems. The development of new high-order numerical schemes for these models using DG-ADER-type schemes or generalized Lax-Wendroff-type schemes will be addressed. High-order, well-balanced numerical schemes for balance laws will be developed, analyzing in detail the presence of discontinuous sources and dry / wet fronts in the shallow water system. Numerical schemes will be developed for problems with degenerate diffusion that appear in multispecies kinetic models related to the deposition of droplets or colloidal substances, as well as in long-time scale sedimentation models. The development of semi-implicit numerical schemes with good balance properties for simulating problems related to sediment carry-over will also be addressed. Finally, the design of new approximate two-dimensional Riemann solvers will be addressed, which are also of interest in the field of computational astrophysics.