Accurate simulation of nonlinear sound waves offers a road to improving a variety of procedures in industry and medicine,
ranging from non-destructive detection of material damages to non-invasive treatments of medical disorders.
In this talk, we will discuss the spatial discretization of Westervelt’s quasi-linear acoustic equation by a high-order discontinuous Galerkin method.
The challenges in the numerical analysis lie in handling the nonlinearity in the model which involves the derivatives in time of the acoustic velocity potential,
and in preventing the model from degenerating. Numerical experiments will illustrate the theoretical convergence results.
This is joint work with Paola F. Antonietti, Ilario Mazzieri (MOX, Politecnico di Milano), Markus Muhr, and Barbara Wohlmuth (TU Munich).