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Multi-dimensional upwind discretization and application to compressible flow

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VKI PHDT 2013-09, Kurt Sermeus, Multi-dimensional upwind discretization and application to compressible flow, ISBN 978-2-87516-057-7, 269 pgs

Multi-dimensional upwind discretization and application to compressible flow

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Multi-dimensional upwind discretization and application to compressible flow
By Kurt Sermeus

PhD Thesis from the von Karman Institute / Université Libre de Bruxelles, January 2013, ISBN 978-2-87516-057-7, 269 pgs


Abstract

This thesis is concerned with the further development and analysis of a class of Computational Fluid Dynamics (CFD) methods for the numerical simulation of com- pressible flows on unstructured grids, known as Residual Distribution (RD). The RD method constitutes a class of discretization schemes for hyperbolic systems of conservation laws, which forms an attractive alternative to the more classical Finite Volume methods, particularly since it allows better representation of the flow physics by genuinely multi-dimensional upwinding and offers second-order accuracy on a compact stencil.

Despite clear advantages of RD schemes, they also have some unexpected anomalies in common with Finite Volume methods and an attempt to resolve them is presented. The most notable anomaly is the violation of the entropy condition, which as a con- sequence allows unphysical expansion shocks to exist in the numerical solution. In the thesis the genuinely multi-dimensional character of this anomaly is analyzed and a multi-dimensional entropy fix is presented and shown to avoid expansion shocks. Another infamous anomaly is the carbuncle phenomenon, an instability observed in many numerical solutions with strong shocks, such as the bow shock on a blunt body in hypersonic flow. The occurence of the carbuncle phenomenon with RD methods is analyzed and a novel formulation for a shock fix, based on an anisotropic diffusion term added in the shock layer, is presented and shown to cure the anomaly in 2D and 3D hypersonic flow problems.

In the present work an effort has been made also to an objective and quantitative assessment of the merits of the RD method for typical aerodynamical engineering applications, such as the transonic flow over airfoils and wings. Validation examples including inviscid, laminar as well as high Reynolds number turbulent flows and comparisons against results from state-of-the-art Finite Volume methods are presented. It is shown that the second-order multi-dimensional upwind RD schemes have an accuracy which is at least as good as second-order FV methods using dimension- by-dimension upwinding and that their main advantage lies in providing excellent monotone shock capturing.

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Manufacturer von Karman Institute for Fluid Dynamics

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