Lagrangian numerical schemes for continuum mechanics

The behavior of a continuum is mathematically described by systems of nonlinear hyperbolic partial differential equations (PDE). Both fluids and solids are modelled by balance laws which are based on first physical principles like conservation of mass, momentum and total energy. A wide range of applications are involved in continuum mechanics, such as environmental and meteorological flows, hydrodynamic and thermodynamic problems, plasma flows as well as the dynamics of many industrial and mechanical processes, namely high energetic interactions of metals involving fluidization, melting and solidification in metallurgy, complex flows like granular flows and flows of viscoplastic fluids (yield stress fluids), which exhibit properties of both elastic solids and viscous fluids. The numerical solution of the discrete governing equations constitutes nowadays a challenging task, thus being a very active research field in the context of applied mathematics. Lagrangian algorithms, in which the computational mesh moves with the material velocity, have become very popular in the last decades due to the excellent properties achieved by these numerical methods in the resolution of moving material interfaces and contact waves. Since the computational mesh is moving with the local fluid velocity, Lagrangian methods are typically affected by much less numerical dissipation compared to classical Eulerian approaches on fixed grids, hence obtaining a more accurate approximation of the solution.
This series of lectures aims at introducing the governing equations for continuum mechanics and at providing an overview of the state-of-the-art numerical methods for the numerical solution of the PDE in the Lagrangian framework.

Date
1st – 3rd December 2020.
Venue
Online seminar on Google Meet platform.
Registration and contacts
Please register by email to walter.boscheri@unife.it before 15th November 2020.
Note
PhD students will be granted 1 CFU for attending the entire series of lectures.

Program
1st December, 9:00 – 11:00 am
Governing equations and models for continuum mechanics Ilya Peshkov
2nd December, 9:00 – 11:00 am
Lagrangian and ALE numerical methods. Raphaël Loubère
3rd December, 9:00 – 11:00 am
ALE and structure-preserving numerical schemes for fluids and solids. Walter Boscheri

Locandina