Gitterfreie Methoden für kinetische Gleichungen auf bewegten Gebieten

• Antragsteller: Professor Dr. Axel Klar
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2019 bis 2024
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 428845667

• Erstellungsjahr: 2024

Zusammenfassung der Projektergebnisse

In this project we concentrated on the development and investigation of Semi-Lagrangian (SL) and Mesh-free Arbitrary-Lagrangian-Eulerian (ALE) methods for moving boundary kinetic problems. The methods have been applied to several technologically relevant problems and the different approaches are compared with each other with respect to approximation quality and efficiency. In particular, a Semi-Lagrangian moving boundary method for the BGK equation developed previously for one spatial dimension has been extended to higher dimensions and a moving grid ALE method for kinetic moving boundary problems has been developed and investigated and applied to a series of benchmark problems.

Projektbezogene Publikationen (Auswahl)

• A meshfree method for the BGK model for rarefied gas dynamics. International Journal of Advances in Engineering Sciences and Applied Mathematics, 11(3), 187-197.
  Tiwari, Sudarshan; Klar, Axel & Russo, Giovanni
  
• Drag force on spherical particle moving near a plane wall in highly rarefied gas. Journal of Fluid Mechanics, 883.
  Goswami, P.; Baier, T.; Tiwari, S.; Lv, C.; Hardt, S. & Klar, A.
  
• Interaction of rigid body motion and rarefied gas dynamics based on the BGK model. Mathematics in Engineering, 2(2), 203-229.
  Tiwari, Sudarshan; Klar, Axel & Russo, Giovanni
  
• Disease contagion models coupled to crowd motion and mesh-free simulation. Mathematical Models and Methods in Applied Sciences, 31(06), 1277-1295.
  Abdul, Salam Parveena Shamim; Bock, Wolfgang; Klar, Axel & Tiwari, Sudarshan
  
• Modelling and Simulations of Moving Droplet in a Rarefied Gas. International Journal of Computational Fluid Dynamics, 35(8), 666-684.
  Tiwari, Sudarshan; Klar, Axel & Russo, Giovanni
  
• A meshfree arbitrary Lagrangian-Eulerian method for the BGK model of the Boltzmann equation with moving boundaries. Journal of Computational Physics, 458, 111088.
  Tiwari, Sudarshan; Klar, Axel & Russo, Giovanni
  
• A mesh-free particle method for continuum modelling of granular flow. Journal of Computational and Applied Mathematics, 438, 115529.
  Tiwari, Sudarshan & Klar, Axel
  
• High-performance computing for the BGK model of the Boltzmann equation with a meshfree Arbitrary Lagrangian-Eulerian (ALE) method
  P. Mariappan, K. Willems, G. Boregowda, S. Tiwari & A. Klar