An energy-dissipative remedy against carbuncle: Application to hypersonic flows around blunt bodies

Garicano‐Mena, Jesús; Lani, Andrea; Deconinck, H.

doi:10.1016/j.compfluid.2016.03.028

Cited by 8 publications

(11 citation statements)

References 10 publications

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“…All simulations are restarted from a first‐order solution obtained with the N scheme. No sign of carbuncle was observed in these simulations …”

Section: Inviscid Resultsmentioning

confidence: 61%

“…Finally, observe how the solution residuals enter in a limit cycle. This behavior is a characteristic of those situations where excessive but uncontrolled dissipation is introduced via a shock‐capturing term; see, eg, the work of Garicano‐Mena et al for another example in the context of artificial viscous terms applied to prevent carbuncle instabilities.…”

Section: Inviscid Resultsmentioning

confidence: 99%

“…The shock‐capturing term has been built around the Lax‐Friedrichs stabilization term, which is possibly the most simple dissipative term available in the RD method framework. The new scheme can be implemented into existing codes with minimally invasive changes and is compatible with other shock‐stabilizing terms, eg, those described in the work of Garicano‐Mena et al…”

Section: Discussionmentioning

confidence: 99%

“…No sign of carbuncle was observed in these simulations. 31 Figure 4 summarizes the Bx scheme results. The region where the N scheme dissipation, ie, the Diss,N l shock-capturing term, is active is shown in Figure 4A: Observe how the dissipation is applied in a very narrow region.…”

Section: Inviscid Ma ∞ = Hypersonic Flow Around a Cylindermentioning

confidence: 99%

“…Residual distribution methods were employed successfully for the discretization and solution of advection-diffusion scalar equations [21][22][23][24] and for the compressible Navier-Stokes equations in the context of transonic aerodynamics 19,[25][26][27] in other works. In the hypersonic field, the method has been applied to double-cone configurations 28,29 and blunt-body problems, both in shock-capturing [30][31][32] and shock-fitting [33][34][35][36] contexts.…”

Section: Introductionmentioning

confidence: 99%

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An enthalpy‐preserving shock‐capturing term for residual distribution schemes

Garicano‐Mena

Degrez

2018

Numerical Methods in Fluids

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Summary In this contribution, we investigate strategies to perform shock‐capturing computation of steady hypersonic flow fields by means of residual distribution schemes. The ultimate objective is the computation of flow solutions for which the correct upstream enthalpy value is recovered in the postshock region. To this end, the parallelism existing between the classical Bx scheme and the stabilized finite element techniques is exploited. The simple Lax‐Friedrichs dissipation term is leveraged to build two new residual distribution schemes. Upon testing on both inviscid and viscous steady problems, solutions obtained with one of the two schemes are shown to recover the correct upstream total enthalpy level in the postshock region. This last scheme provides also improved wall pressure and skin friction predictions; heat transfer predictions are, unfortunately, similar to those offered by the Bx scheme. A conjecture for explaining this behavior is exposed.

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“…All simulations are restarted from a first‐order solution obtained with the N scheme. No sign of carbuncle was observed in these simulations …”

Section: Inviscid Resultsmentioning

confidence: 61%

Section: Inviscid Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Inviscid Ma ∞ = Hypersonic Flow Around a Cylindermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An enthalpy‐preserving shock‐capturing term for residual distribution schemes

Garicano‐Mena

Degrez

2018

Numerical Methods in Fluids

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Stability analysis of the carbuncle phenomenon and the sonic point glitch

Agrawal

Srinivasan

2017

Sādhanā

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Upwinding allows for accurate, non-oscillatory capturing of shocks waves; however, many Riemann solvers (both exact and approximate) suffer from some sort of numerical instability. One of the most mysterious and least understood of these is the carbuncle phenomenon. In the present study, we analyse the closely allied ''simplified carbuncle'' problem, also known as the 2D shock stability problem or the 1.5D carbuncle problem. Motivated by the existence of some recently derived schemes that do not exhibit the instability, we perform a thorough stability analysis and extend previous studies by analysing the pseudo-spectra and hence the effects of non-normality in causing this instability. Our results establish that, contrary to previous indications in the literature, a non-linear mechanism is responsible for the instability. In order to understand the nature of this non-linear mechanism better, we perform a non-linear analysis of the sonic glitch, which shares some common features with the carbuncle. We provide two previously unknown results. Firstly, we show that even the ''entropy-satisfying'' Godunov scheme violates the entropy condition in the sonic glitch. Secondly, we provide a more accurate definition for the entropy condition for scalar conservation laws that supports the previous claim. We conjecture that a similar non-linear anti-dissipative mechanism might be responsible in triggering the carbuncle. This work is expected to lead to a better understanding of possible unphysical behaviour in Riemann solvers and thus help in the design of better solvers for high-Reynolds-number flows.

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