Hybrid central-upwind finite volume schemes for solving the Euler and Navier–Stokes equations

Jiang, Zhenhua; Yan, Chao; Yu, Jian; Li, Yansu

doi:10.1016/j.camwa.2016.08.022

Cited by 6 publications

(1 citation statement)

References 26 publications

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“…The k-stage (k = m + 1) BVD-CD algorithm is formulated as follows. (17) and from the THINC function qTk i (x) with a steepness β k as…”

Section: The Bvd-cd Algorithmmentioning

confidence: 99%

A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows

Deng¹,

Jiang²,

Vincent³

et al. 2020

Preprint

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The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-controllable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. The new scheme employs a polynomial of n-degree and non-polynomial THINC ( Tangent of Hyperbola for INterface Capturing) functions of m-level steepness as reconstruction candidates. These reconstruction candidates are denoted as PnTm. From these candidates, the piecewise reconstruction function is selected through the boundary variation diminishing (BVD) algorithm. Unlike other shock-capturing techniques, the BVD algorithm effectively suppresses numerical oscillations without introducing excess numerical dissipation. Then, a controllable dissipation (CD) algorithm is designed for scale-resolving simulations. This novel paradigm of shock-capturing scheme is named as PnTm-BVD-CD. The proposed PnTm-BVD-CD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of PnTm-BVD-CD can be effectively controlled between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter λ. Thirdly, with λ = 0.5 the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with dissipation controllable algorithm through so-called implicit LES (ILES) approach. Through simulating benchmark tests involving multi-scale flow structures and comparing with other central-upwind schemes, the superiority of the proposed scheme is evident. Thus, this work provides an alternative scheme for solving multi-scale problems in high speed compressible flows.

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“…The k-stage (k = m + 1) BVD-CD algorithm is formulated as follows. (17) and from the THINC function qTk i (x) with a steepness β k as…”

Section: The Bvd-cd Algorithmmentioning

confidence: 99%

A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows

Deng¹,

Jiang²,

Vincent³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Effect of time integration scheme in the numerical approximation of thermally coupled problems: From first to third order

Ortega

Castillo

Cabrales

et al. 2021

Computers & Mathematics with Applications

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Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

Huang

Jiang

Lou

et al. 2023

Chinese Journal of Aeronautics

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Hybrid central-upwind finite volume schemes for solving the Euler and Navier–Stokes equations

Cited by 6 publications

References 26 publications

A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows

A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows

Effect of time integration scheme in the numerical approximation of thermally coupled problems: From first to third order

Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

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