My Way: A Computational Autobiography

Roe, Philip L.

doi:10.1007/s42967-019-00021-0

Cited by 1 publication

(3 citation statements)

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“…Here |C j stands for the measure of C j , |C j | = x j+1/2 − x j−1/2 . As in [8], I introduce the quantities defined for the element K j+1/2 = [x j , x j+1 ] whatever j ∈ Z by:…”

Section: A Different Point Of Viewmentioning

confidence: 99%

“…The control volumes in this case are defined as the median cell, see figure 2. We concentrate on the approximation of div f , see equation (8). Since the boundary of C σ is a closed polygon, the scaled outward normals n γ to ∂C σ sum up to 0:…”

Section: A Different Point Of Viewmentioning

confidence: 99%

“…In (10), the first term of the right hand side is the Galerkin term. It is obtained by multiplying (8) by the test function w h , apply the divergence theorem and take into account the continuity of the elements of v h accross the edges of the mesh. The last term corresponds to the boundary conditions.…”

Section: Many Schemes Are Not Naturally Written In a Finite Volume Formmentioning

confidence: 99%

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The Notion of Conservation for Residual Distribution Schemes (or Fluctuation Splitting Schemes), with Some Applications

Abgrall

2019

Commun. Appl. Math. Comput.

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In this paper, we discuss the notion of discrete conservation for hyperbolic conservation laws. We introduce what we call a fluctuation splitting schemes (or residual distribution, also RDS) and show on several examples how this cal lead to new development. In particular, we show that most, if not all known schemes can be rephrased in flux form, and also show how to satisfy additional conservation laws. This review paper is built on [1,2,3,4,5].This paper is also a direct consequence of the work of P.L. Roe, in particular [6,7] where the notion of conservation I will discussed is first introduced. In [8], P.L. Roe mentions the Hermes project, and the role of Dassault Aviation in it. I was suggested by Bruno Stoufflet, now Vice-President R&D and advanced business in this company, to have a detailed look at [7]. To be honnest, at the time, I did not understood anything, and this was the case for several years. I was lucky to work with Katherine Mer, at the time a postdoc, now research engineer at CEA, and she helped me a lot in starting to understand this notion of conservation. The present contribution can be seen as what I managed to understand after many years playing around the very productive notion of residual distribution schemes (or fluctuation splitting schemes), introduced by P. L. Roe.

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“…Here |C j stands for the measure of C j , |C j | = x j+1/2 − x j−1/2 . As in [8], I introduce the quantities defined for the element K j+1/2 = [x j , x j+1 ] whatever j ∈ Z by:…”

Section: A Different Point Of Viewmentioning

confidence: 99%

Section: A Different Point Of Viewmentioning

confidence: 99%

Section: Many Schemes Are Not Naturally Written In a Finite Volume Formmentioning

confidence: 99%

See 1 more Smart Citation

The Notion of Conservation for Residual Distribution Schemes (or Fluctuation Splitting Schemes), with Some Applications

Abgrall

2019

Commun. Appl. Math. Comput.

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My Way: A Computational Autobiography

Abstract: In this paper, the author recounts his forty-year plus struggle to find a sound basis for understanding the computational fluid dynamics of compressible flow.

Cited by 1 publication

References 40 publications

The Notion of Conservation for Residual Distribution Schemes (or Fluctuation Splitting Schemes), with Some Applications

The Notion of Conservation for Residual Distribution Schemes (or Fluctuation Splitting Schemes), with Some Applications

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