Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks
Nair, Nirmal Jayaprasad
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https://hdl.handle.net/2142/101093
Description
Title
Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks
Author(s)
Nair, Nirmal Jayaprasad
Issue Date
2018-04-26
Director of Research (if dissertation) or Advisor (if thesis)
Balajewicz, Maciej
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
parametric model order reduction
steady state residual
shock
hyperbolic PDE
Abstract
In this thesis, a new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.
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