Seminario "La Ricerca ... Ti cerca!"

Il giorno 14 marzo alle 12 presso l’aula G il dottor Bernardo Collufio (GSSI) terrà un seminario dal titolo:

The Runge-Kutta semi-lagrangian scheme for solving BGK equation

Abstract:

The BGK equation plays a crucial role in gas dynamics, approximating the effect of collisions near the equilibrium state. Over the years, several numerical methods have been developed to solve this equation efficiently.

Eulerian methods, which involve direct discretization on a fixed grid, offer high accuracy and may preserve fundamental system properties like positivity. However, they are constrained by the CFL condition, which can limit efficiency. Particle methods, such as Direct Simulation Monte Carlo (DSMC), provide advantages in handling convection terms without excessive memory usage or CFL restrictions. While these methods automatically preserve macroscopic moments, they suffer from statistical noise, requiring extensive computations for accurate solutions, particularly near thermodynamic equilibrium.

Recently, semi-Lagrangian schemes have gained attention due to their accuracy and stability properties. These methods use a Cartesian mesh but handle convection through a Lagrangian formulation, applying time integration along characteristic trajectories. They offer relaxed CFL constraints and improved efficiency; however, they do not always maintain the physical relevance of the model, as they may fail to preserve key properties such as conservation of moments and positivity.

In this talk, I will review the Runge-Kutta semi-lagrangian scheme for the BGK equation (Russo, Groppi, Stracquadanio, 2015) and discuss the existing techniques aimed to ensure physical properties such as moments conservation and positivity of solution.