IMEX methods for diffusively corrected multi-species kinematic flow models
Presented by Prof. Pep MULET-MESTRE
Type: Oral presentation
Track: Numerical Methods for Partial Differential Equations
Explicit schemes for the solution of nonlinear convection-diffusion equations have severe time step restrictions for accurate simulations with dominant diffusion. Therefore Implicit-explicit (IMEX) methods are suitable for the solution of those equations, since the stability restrictions, coming from the explicitly treated convective part, are much less severe than those that would be deduced from an explicit treatment of the diffusive term. These schemes usually combine an explicit Runge-Kutta scheme for the time integration of the convective part with a diagonally implicit one for the diffusive part. The application of these schemes to multi-species kinematic flow models with strongly degenerate diffusive corrections requires the solution of highly nonlinear and non-smooth systems of algebraic equations. We propose a regularization of the diffusion coefficients in the model and suitable techniques for getting a globally convergent Newton-Raphson-based nonlinear solver for those equations. Numerical examples arising from models of polydisperse sedimentation and multi-class traffic flow confirm the efficiency of the methods proposed.
Location: Koper, Slovenia
- Prof. Pep MULET-MESTRE Departament de Matemàtica Aplicada, Universitat de València