Mesh-free methods with least squares approximations for kinetic equations with moving boundaries

• Applicant: Professor Dr. Axel Klar
• Subject Area: Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 428845667

• Final Report Year: 2024

Final Report Abstract

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.

Publications

• 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