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Lattice Boltzmann Methods for Partial Differential Equations

Simonis, Stephan ORCID iD icon 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract (englisch):

Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. ... mehr


Volltext §
DOI: 10.5445/IR/1000161726
Veröffentlicht am 13.09.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Publikationsdatum 13.09.2023
Sprache Englisch
Identifikator KITopen-ID: 1000161726
Verlag Karlsruher Institut für Technologie (KIT)
Umfang vi, 204 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 28.06.2023
Schlagwörter lattice Boltzmann methods, partial differential equations, relaxation systems, relaxation functions, numerical analysis, computational analysis, spectral analysis, scheme construction, stability, limit consistency, convergence, accuracy, computational fluid dynamics, Navier–Stokes equations, turbulence, temporal large eddy simulation, statistical solutions, Euler equations, Cahn–Hilliard equation, advection–diffusion equation, free energy functionals, binary fluid flow simulation, fluid flow in porous media, exploratory computing, high performance computing
Referent/Betreuer Krause, Mathias J.
Mishra, Siddhartha
Reis, Timothy
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