Multiwavelets and outlier detection for troubled-cell indication in discontinuous Galerkin methods

This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: non-physical...

Automated Parameters for Troubled-Cell Indicators Using Outlier Detection

In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...

A level set method for particle dissolution in a binary alloy

A mathematical model is proposed for the dissolution of stoichiometric particles in binary alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. The Level Set method is used to capture the interface location implicitly. The front velocity, only dened on the moving interface, should be advected to the...