A non-parametric discontinuous Galerkin formulation of the integral boundary layer equations with strong viscous-inviscid coupling

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Aeronautics and Astronautics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Zhang, Shun (Aerospace scientist) Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Steven R. Allmaras.

• Aeronautics and Astronautics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/119272

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/119272