High-order discontinuous Galerkin Boltzmann solutions for low mach aerodynamics

Date

2023-9-07

Author

Akad, Ozan

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This thesis advances the understanding and computational techniques of low Mach number aerodynamics by applying high-order discontinuous Galerkin (DG) solutions to the Boltzmann-BGK equation. Leveraging the power of the libparanumal framework, this study provides comprehensive insights into the behavior of flows at low Mach numbers. The core methodology involves discretizing the Boltzmann-BGK equation in velocity space by employing the Hermite polynomials, resulting in a system of equations governing flow motion. The complicated system is efficiently addressed using the discontinuous Galerkin technique, which provides strong numerical solutions that accurately describe the underlying physics. Incorporating a perfectly matched layer (PML), a method crucial in eradicating unwanted artifacts resulting from problem boundaries, addresses the difficulties posed by boundary oscillations. The effectiveness of the suggested methodology is thoroughly investigated and supported through meticulous analysis of benchmark and low Mach aerodynamic conditions and drawing comparisons between the obtained solutions and existing data within the literature. This thesis contributes to the computation of low Mach number aerodynamics by carefully combining high-order discontinuous Galerkin methods, the Galerkin Boltzmann formulation, and the perfectly matched layer technique. The gaining of knowledge derived from the results and the subsequent comparisons with known data contribute to advancing our understanding of flow behaviors. Moreover, this progress facilitates the development of more accurate and reliable simulations for engineering applications.

Subject Keywords

Computational fluid dynamics, Discontinuous Galerkin method, BGK-Boltzmann equation, Perfectly matched layer, Libparanumal, Low mach aerodynamics

URI

https://hdl.handle.net/11511/105427

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Graduate School of Natural and Applied Sciences, Thesis