Project Details
Projekt
High-order asymptotic preserving mesh-free methods for multi-species kinetic equations based on moving least squares discretizations
Applicant
Professor Dr. Axel Klar
Subject Area
Mathematics
Term
since 2025
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 563035366
The present proposal aims at developing and improving a mesh-free moving least squares ALE method for the kinetic BGK equation. A higher order spatial differencing in a generalized finite difference framework will be based on a combination of different reconstruction approaches with the MOOD technology to prevent oscillatory behavior of the solutions. For the reconstruction we investigate a MUSCL-type approach (transferred to the generalized Finite-Difference case) using moving least squares reconstructions. For the time discretization appropriate IMEX schemes are used. Moreover, we plan to develop an asymptotic preserving (AP) time discretization for the kinetic equations in the Low-Mach number (incompressible Navier-Stokes) limit. This requires a suitable micro-macro decomposition of the kinetic problem combined with an appropriate IMEX approach. Finally, we plan to extend the previous points to the case of multi-species BGK equations. Applications to be tackled during this proposal include in particular separation problems for chiral nano-particles in a multi-component gas. For larger scale computations a GPU based implementation of the code is planned continuing ongoing work.
DFG Programme
Research Grants
International Connection
India, Italy, United Kingdom
