Repository logo

Theses and Dissertations

Permanent URI for this collection

https://hdl.handle.net/10217/100472

Browse

Browsing Theses and Dissertations by Subject "adaptive mesh refinement"

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    A fourth-order finite volume algorithm with adaptive mesh refinement in space and time for multi-fluid plasma modeling
    (Colorado State University. Libraries, 2022) Polak, Scott E., author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Tomasel, Fernando, committee member; Ghosh, Debojyoti, committee member; Bangerth, Wolfgang, committee member
    Improving our fundamental understanding of plasma physics using numerical methods is pivotal to the advancement of science and the continual development of cutting-edge technologies such as nuclear fusion reactions for energy production or the manufacturing of microelectronic devices. An elaborate and accurate approach to modeling plasmas using computational fluid dynamics (CFD) is the multi-fluid method, where the full set of fluid mechanics equations are solved for each species in the plasma simultaneously with Maxwell's equations in a coupled fashion. Nevertheless, multi-fluid plasma modeling is inherently multiscale and multiphysics, presenting significant numerical and mathematical stiffness. This research aims to develop an efficient and accurate multi-fluid plasma model using higher-order, finite-volume, solution-adaptive numerical methods. The algorithm developed herein is verified to be fourth-order accurate for electromagnetic simulations as well as those involving fully-coupled, multi-fluid plasma physics. The solutions to common plasma test problems obtained by the algorithm are validated against exact solutions and results from literature. The algorithm is shown to be robust and stable in the presence of complex solution topology and discontinuities, such as shocks and steep gradients. The optimizations in spatial discretization provided by the fourth-order algorithm and adaptive mesh refinement are demonstrated to improve the solution time by a factor of 10 compared to lower-order methods on fixed-grid meshes. This research produces an advanced, multi-fluid plasma modeling framework which allows for studying complex, realistic plasmas involving collisions and practical geometries.
  • Thumbnail Image
    ItemOpen Access
    Large-eddy simulation of compressible flows using the stretched-vortex model and a fourth-order finite volume scheme on adaptive grids
    (Colorado State University. Libraries, 2022) Walters, Sean, author; Guzik, Stephen, advisor; Gao, Xinfeng, advisor; Randall, David, committee member; Yalin, Azer, committee member
    State-of-the-art engineering workflows are becoming increasingly dependent on accurate large-eddy simulations (LES) of compressible, turbulent flows for off-design conditions. Traditional CFD algorithms for compressible flows rely on numerical stabilization to handle unresolved physics and/or steep gradient flow features such as shockwaves. To reach higher levels of physical-fidelity than previously attainable, more accurate turbulence models must be properly incorporated into existing, high-order CFD codes in a manner that preserves the stability of the underlying algorithm while fully realizing the benefits of the turbulence model. As it stands, casually combining turbulence models and numerical stabilization degrades LES solutions below the level achievable by using numerical stabilization alone. To effectively use high-quality turbulence models and numerical stabilization simultaneously in a fourth-order-accurate finite volume LES algorithm, a new method based on scale separation is developed using adaptive grid technology for the stretched-vortex subgrid-scale (SGS) LES model. This method successfully demonstrates scheme-independent and grid-independent LES results at very-high-Reynolds numbers for the inviscid Taylor-Green vortex, the temporally-evolving double-shear-flow, and decaying, homogeneous turbulence. Furthermore, the method clearly demonstrates quantifiable advantages of high-order accurate numerical methods. Additionally, the stretched-vortex LES wall-model is extended to curvilinear mapped meshes for compressible flow simulations using adaptive mesh refinement. The capabilities of the wall-model combined with the stretched-vortex SGS LES model are demonstrated using the canonical zero-pressure-gradient flat-plate turbulent boundary layer. Finally, the complete algorithm is applied to simulate flow-separation and reattachment over a smooth-ramp, showing high-quality solutions on extremely coarse meshes.