## Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations (1996)

Venue: | COMPUTATIONAL FLUID DYNAMICS JOURNAL |

Citations: | 9 - 7 self |

### BibTeX

@ARTICLE{Giles96analysisof,

author = {M. B. Giles},

title = {Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations},

journal = {COMPUTATIONAL FLUID DYNAMICS JOURNAL},

year = {1996},

volume = {5},

number = {2},

pages = {247--258}

}

### OpenURL

### Abstract

Insight into the accuracy of steady shock-capturing CFD methods is obtained through analysis of a simple problem involving steady transonic flow in a quasi-1D diverging duct. It is proved that the discrete solution error on either side of the shock is O(h n) where n is the order of accuracy of the conservative finite volume discretisation. Furthermore, it is shown that provided that n 2 then the error in approximating R p dx is O(h 2). This result is in contrast to the general belief that shocks in 2D and 3D Euler calculations lead to first order errors, which motivates much of the research into grid adaptation methods.

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Citation Context ...mputing Laboratory Numerical Analysis Group Wolfson Building Parks Road Oxford, England OX1 3QD E-mail: giles@comlab.oxford.ac.uk April, 1997 2 1 Introduction The paper by Jameson, Schmidt and Turkel =-=[5]-=- is a landmark in the development of CFD methods, being one of the first papers on the solution of the multidimensional Euler equations in conservative form by a time-marching method. Runge-Kutta time... |

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Citation Context ...e size of cells crossed by the shock. With structured grids this is usually accomplished by redistributing the grid nodes. With unstructured grids, in which Jameson has again played a pioneering role =-=[3, 4]-=-, it is usually accomplished by grid refinement, subdividing triangles or tetrahedra into a number of smaller triangles or tetrahedra. One important aspect of grid adaptation is the criterion used to ... |

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