Unstructured h-adaptive finite volume schemes for compressible viscous fluid flow

The current thesis presents a novel methodology for solving the Euler and Reynolds-averaged Navier-Stokes equations for compressible fluid flow. The central objective of the presented research is to realize adaptively generated discretizations that are able to resolve the physically relevant phenomena at the expense of possibly few degrees of freedom and correspondingly reduced storage demands. This requires a careful coordination of the core ingredients namely the discretization of the underlying system of partial differential equations, the generation and management of suitable meshes and the adaptation mechanisms. Preference is given to curvilinear meshes, which are embedded into a multiblock concept. A key idea is to represent such meshes by a parametric mapping from the computational domain into the physical domain by means of B-spline techniques. The mesh is locally adapted to the solution according to the concept of h-adaptation. Adaptation criteria are based on multiresolution techniques. The spatial discretization is based on a finite volume scheme for two- and three-dimensional flow problems. Thereby, the grid is considered as a fully unstructured mesh, composed of simply connected elements with otherwise arbitrary topology. The method is of second order accuracy in space and time. In order to account for the directed transport of information within the solution domain, the convective fluxes are discretized with upwind schemes. Diffusive fluxes are discretized in a quasi-central fashion, specifically suited for discretizations on unstructured grids. Turbulence is considered by the Spalart-Allmaras one-equation model. Time integration is based on a fully implicit Newton-Krylov type approach, which is suitable for stationary and non-stationary flows. A local preconditioning technique is employed in conjunction with the AUSMDV(P) upwind method to operate effectively within the quasi-incompressible low Mach number regime. The proposed method has been validated for a wide range of applications of engineering interest. Inviscid flows for two-dimensional and three-dimensional configurations, including complete aircraft configurations, as well as turbulent flows about planar geometries have been studied. The considered Mach number regime ranges from quasi-incompressible fluid flow at Mach=0.01 up to hypersonic flow at Mach=8.15. Major emphasis has been devoted to applications of relevance to aerodynamics of wings in cruise configuration as well as in high-lift configuration. Detailed studies have demonstrated the benefits of local grid adaptation to significantly improve the solution accuracy and to reduce the number of grid points by several orders of magnitude in some cases, compared with non-adaptive grids.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2003

Author dc:creator

• Bramkamp, Frank Dieter

Contributors dc:contributor

• Ballmann, Josef

• info:eu-repo/classification/ddc/530
• Kompressible Strömung
• Viskose Strömung
• Numerische Strömungssimulation
• Finite-Volumen-Methode
• Adaptives Verfahren
• Physik
• numerische simulation
• finite-volumen
• adaption

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-123525%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:61913