In this talk we aim to describe well-balanced Lagrange-projection schemes that can be exploited for the numerical simulation of not only geophysical but also biological flows. In a few words, such met...
This talk describes a novel subface flux-based Finite Volume (FV) method for discretizing multi-dimensional hyperbolic systems of conservation laws of general unstructured grids. The subface flux nume...
We discuss models for reaction-diffusion phenomena based on hyperbolic equations. The standard approach uses parabolic systems, which are well suited to explain events such as heat transmission in clo...
We present our recent result on the error analysis of the finite volume Godunov method when applied to multidimensional Euler equations of gas dynamics. The main tool is to use a problem-related metri...
Solutions of many nonlinear PDE systems reveal a multiscale character; thus, their numerical resolution presents some major difficulties. Such problems are typically characterized by a small parameter...
In this work, we propose a well-balanced Implicit-Explicit Runge-Kutta scheme for the efficient simulation of the Baer-Nunziato model at all-Mach regimes. The numerical method is based on the explicit...
Modelling of gas networks, fluid-structure systems and multi-phase flows requires development of coupling techniques. Recent works on coupling of hyperbolic systems of conservation laws based on solvi...
We present a kinetic model for opinion dynamics depending on the presence of social media contacts. Firstly, we describe how to model the evolution of the density of contacts starting from the microsc...
We propose a level set method to reconstruct unknown surfaces from a point cloud, without assuming that the connections between points are known. The formulation of the problem follows the variational...
We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof ...
