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This monograph stems from my PhD thesis in Computational Fluid Dynamics at MIT, supervised by Professor Earll Murman. It presents a new finite element algorithm for solving the steady Euler equations that describe the flow of an inviscid, compressible, ideal gas. The algorithm employs a finite element spatial discretization combined with Runge-Kutta time integration to achieve steady state. It demonstrates that finite difference and finite volume methods can be derived from finite element principles. A higher-order biquadratic approximation is introduced, and several test problems are computed to verify the algorithms. The work includes the development and verification of adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements, showing CPU savings ranging from 2 to 16 times, with biquadratic elements offering additional savings of 2 to 6 times. An analysis of the dispersive properties of various discretization methods for the Euler equations is provided, yielding results for predicting dispersive errors. The adaptive algorithm is applied to scramjet inlet flows in two and three dimensions, highlighting the diverse physics involved. Additionally, the monograph addresses design and implementation challenges of adaptive finite element algorithms on vector and parallel computers.
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Adaptive finite element solution algorithm for the Euler equations, Richard A. Shapiro
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- Année de publication
- 1991
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