A non-parametric discontinuous Galerkin formulation of the integral boundary layer equations with strong viscous-inviscid coupling
Author(s)Zhang, Shun, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Steven R. Allmaras.
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A non-parametric discontinuous Galerkin (DG) finite-element formulation is developed for the integral boundary layer (IBL) equations with strong viscous-inviscid coupling. This DG formulation eliminates the need of explicit curvilinear coordinates in traditional boundary layer solvers, and thus enables application to complex geometries even involving non-smooth features. The usual curvilinear coordinates are replaced by a local Cartesian basis, which is conveniently constructed in the DG finite-element formulation. This formulation is also applicable to the general convection-source type of partial differential equations defined on curved manifolds. Other benefits of DG methods are maintained, including support for high-order solutions and applicability to general unstructured meshes. For robust solution of the coupled IBL equations, a strong viscous-inviscid coupling scheme is also proposed, utilizing a global Newton method. This method provides for flexible and convenient coupling of viscous and inviscid solutions, and is readily extensible to coupling with more disciplines, such as structural analysis. As a precursor to the three-dimensional strongly-coupled IBL method, a two-dimensional IBL solver coupled with a panel method is implemented. Numerical examples are presented to demonstrate the viability and utility of the proposed methodology.
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 117-121).
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Massachusetts Institute of Technology
Aeronautics and Astronautics.