Contributed Talk
Projective integration schemes for nonlinear degenerate parabolic systems
Université Côte d'Azur, France - University La Sapienza, Rome, Italy
Abstract
In this talk we present a general high-order fully explicit scheme based on projective integration methods to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the advection-diffusion equation, where projective integration method is introduced as time integrator to deal with the stiff relaxation term. This approach exploits the clear gap in the eigenvalues spectrum of the kinetic equation, taking into account a sequence of small time steps to damp out the stiff components, followed by an extrapolation step over a large time interval. The time step restriction on the projective step is similar to the CFL condition for advection-diffusion equations. The scheme is validated against some test cases, providing solutions in one and two spatial dimensions.