A matrix stability analysis of the carbuncle phenomenon

Dumbser, Michael; Moschetta, Jean‐Marc; Gressier, Jérémie

doi:10.1016/j.jcp.2003.12.013

Cited by 157 publications

(116 citation statements)

References 34 publications

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“…However, when using Riemann solvers there is no implicit dissipation that exists inside the shock, and the only dissipation present is artificial dissipation. Xu and Hu (1998) and Xu (1999) It has also been shown by Dumbser et al (2004) that the source of the carbuncle phenomenon is immediately upstream of the shock and the instability is convected downstream. This would explain why shock fitting schemes do not suffer from the carbuncle phenomenon, since they only capture the flow on the downstream side of the shock.…”

Section: Effect Of Artificial Viscosity On the Carbuncle Phenomenonmentioning

confidence: 96%

“…Liou (2000) proposes that Riemann solvers can be designed that eliminate the pressure dependence of the mass flux; and that existing Riemann schemes can be modified to satisfy this hypothesis. Unfortunately, directly canceling the pressure terms from the mass flux degrades the stability of the Riemann solver and contradicts a fundamental physical principle; a pressure difference produces a mass flux [Dumbser et al 2004]. Liou's hypothesis has led to the development of the AUSM (Advected Upstream Splitting Method) scheme [Liou 2000] and other variants of the AUSM scheme that have this property.…”

Section: Proposed Cures Using Riemann Solversmentioning

confidence: 99%

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Effects-Based Operations at the Operational Level of War: Exploring the Living System Alternative

Dees¹

2008

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information SPONSORING/MONITORING AGENCY REPORT NUMBER(S) AFRL-RB-WP-TR-2008-3133 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTESPAO Case Number: WPAFB 08-3904; Clearance Date: 02 Jul 2008. Report contains color. ABSTRACTThis work is part of a project to more accurately model hypersonic flow. A number of issues in hypersonic flow are addressed. The first issue addressed is that of air properties at increased temperatures. Thermodynamic and transport properties of chemical equilibrium air are found for temperatures up to 30,000 K for a pressure range from 1x10 -4 to 100 atm. This work also covers adding equilibrium air chemistry to the computational fluid dynamics computer code known as AVUS. The second issue addressed is the carbuncle problem. A grid study is performed and recommendations as to what types of structured grids should be used to reduce the carbuncle problem are made. Grid aspect ratio and the alignment of the grid to the flow can be used to reduce the effects of the carbuncle phenomenon. Another mechanism causing the carbuncle phenomenon is the alignment of the grids with the shock. The third issue addressed is the domain of applicability of the perfect gas model, equilibrium air model, nonequilibrium air model, and thermo-chemical nonequilibrium air model. A computational study is carried out using AVUS to determine the regions of applicability of these air models for a blunt body at various velocities and altitudes.Full ABSTRACT (full)This work is part of a project to more accurately model hypersonic flow. A number of issues in hypersonic flow are addressed. The first issue addressed is that of air properties at increased temperatures. In particular the thermodynamic and transport properties of chemical equilibrium air are found for temperatures up to 30,000 K for a pressure range from 1x10 -4 to 100 atm. This work provides properties at slightly higher temperatures for the lower pressure region than can be found in the literature. This work also covers adding equilibrium air chemistry to the computational fluid dynamics computer code known as AVUS. The second issue addressed is commonly referred to as the carbuncle phenomenon. The carbuncle phenomenon is a numerical instability that affects the capturing of strong shocks when using a Riemann solver with low numerical dissipation. The carbuncle phenomenon manifests itself in the inability to compute uniform flow conditions downstream of a normal o...

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Section: Effect Of Artificial Viscosity On the Carbuncle Phenomenonmentioning

confidence: 96%

Section: Proposed Cures Using Riemann Solversmentioning

confidence: 99%

Effects-Based Operations at the Operational Level of War: Exploring the Living System Alternative

Dees¹

2008

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“…The problem is illustrated by the solution to a modified version of Sod's shock tube problem [52,55] (20) with the initial discontinuity located at x = −0.4. Figure 1 shows the results produced by the FCT method with and without our sonic fix.…”

Section: Sonic Fixmentioning

confidence: 99%

“…The result is a complex interaction and results in an irregular Mach reflection. Numerically, this flow can cause a carbuncle like instability [47,20] for some numerical methods if proper care is not taken. Traditionally this test problem has been solved by inclining the incident shock to a Cartesian grid and using special boundary conditions to simulate the transition region at the start of the ramp.…”

Section: Irregular Mach Reflection Of a Strong Shockmentioning

confidence: 99%

An Evaluation of a Structured Overlapping Grid Implementation of FCT for High-Speed Flows

Banks

Shadid

2012

Scientific Computation

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“…On the other hand, schemes taken from the ÿrst category are attractive for viscous computations but turn out to be sensitive to the carbuncle phenomenon at various degrees [1,2] with very few exceptions [3]. It has been recently observed [4] that the internal shock structure is essential to trigger the carbuncle phenomenon. This is consistent with former heuristic explanations for the onset of the carbuncle phenomenon [5] in which intermediate shock points play an important role to generate shock instabilities.…”

Section: Introductionmentioning

confidence: 99%

Shock wave numerical structure and the carbuncle phenomenon

Chauvat

Moschetta

Gressier

2005

Numerical Methods in Fluids

108

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SUMMARYSince the development of shock-capturing methods, the carbuncle phenomenon has been reported to be a spurious solution produced by almost all currently available contact-preserving methods. The present analysis indicates that the onset of carbuncle phenomenon is actually strongly related to the shock wave numerical structure. A matrix-based stability analysis as well as Euler ÿnite volume computations are compared to illustrate the importance of the internal shock structure to trigger the carbuncle phenomenon.

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A matrix stability analysis of the carbuncle phenomenon

Cited by 157 publications

References 34 publications

Effects-Based Operations at the Operational Level of War: Exploring the Living System Alternative

Effects-Based Operations at the Operational Level of War: Exploring the Living System Alternative

An Evaluation of a Structured Overlapping Grid Implementation of FCT for High-Speed Flows

Shock wave numerical structure and the carbuncle phenomenon

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