September 11, 2023
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Length-scales for efficient CFL conditions in high-order methods with distorted meshes: Application to local-timestepping for p-multigrid

Publicated to: COMPUTERS & FLUIDS. 265 106011- - 2023-10-30 265(), DOI: 10.1016/j.compfluid.2023.106011

Authors:

Joshi, S; Kou, JQ; de Mendoza, AH; Puri, K; Hirsch, C; Rubio, G; Ferrer, E
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Affiliations

Cadence Design Syst Ltd, Chaussee Hulpe 189, B-1170 Brussels, Belgium - Author
Cadence Design Systems - Author
Rhein Westfal TH Aachen, AIA, Wullnerstr 5a, D-52062 Aachen, Germany - Author
Rheinisch-Westfalische Technische Hochschule Aachen - Author
Univ Politecn Madrid, Ctr Computat Simulat, Campus Montegancedo, E-28660 Madrid, Spain - Author
Univ Politecn Madrid, Sch Aeronaut, ETSIAE, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain - Author
Universidad Politécnica de Madrid - Author
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Abstract

We propose a strategy to estimate the maximum stable time-steps for explicit time-stepping methods for hyperbolic systems in a high-order flux reconstruction framework. The strategy is derived through a von-Neumann analysis (VNA) framework for the advection–diffusion equation on skewed two- and three-dimensional meshes. It directly incorporates the spatial polynomial- and mesh-discretization in estimating the convective and diffusive length-scales. The strategy is extended to the density-based Navier–Stokes system of equations, taking into account the omnidirectionality of the speed of sound. We compare the performance of this strategy with three other popular choices of length-scales across a wide range of polynomial-orders, meshes of drastically varying cell-quality, and flow-physics. The proposed strategy shows robust behavior across all test-scenarios with limited variation of the maximum stable CFL-number (0.1 to 1) for polynomial-orders 1 through 10, unlike other strategies where the CFL-number varies sharply. Finally, we show the advantage of the proposed methodology for local-timestepping for p-multigrid through a RANS-modeled steady-state turbulent flow case, on a mesh with large disparity of mesh elements and aspect ratios.
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Keywords

cfldistortedflux reconstructionhigh-orderskewedtimestepCflDiscontinuous galerkin schemeDistortedHigh-orderLength-scaleSkewedTimestep

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal COMPUTERS & FLUIDS due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2023, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Engineering (Miscellaneous).

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.03. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 13, 2025)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.03 (source consulted: FECYT Mar 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2026-04-24, the following number of citations:

  • WoS: 6
  • Scopus: 6
  • Google Scholar: 4
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-24:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/86467/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 134
  • Downloads: 32
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Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Belgium; Germany; United States of America.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (JOSHI, SAUMITRA VINAY) and Last Author (FERRER VACCAREZZA, ESTEBAN).

the author responsible for correspondence tasks has been JOSHI, SAUMITRA VINAY.

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