Ricerc@Sapienza

In the present paper, a Vortex Particle Method is combined with a Boundary Element Method for the study of vis- cous incompressible planar flow around solid bodies. The method is based on Chorins operator splitting approach for the Navier Stokes equations written in vorticity–velocity formulation, and consists of an advection step fol- lowed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz–Hodge Decomposition, while the no-slip condition is enforced by an indirect boundary integral equation.

This paper deals with the numerical (finite volume) approximation of reaction–diffusion systems with relaxation, among which the hyperbolic extension of the Allen–Cahn equation – given by τ ∂ttu +1−τ f (u)∂tu −μ∂xxu = f (u), where τ, μ >0and fis a cubic-like function with three zeros – represents a notable prototype. Appropriate discretizations are constructed starting from the kinetic interpretation of the model as a particular case of reactive jump process, given by the substitution of the Fourier’s law with the Maxwell–Cattaneo’s law.