Healing of shock instability for Roe's flux‐difference splitting scheme on triangular meshes

Phongthanapanich, Sutthisak; Dechaumphai, Pramote

doi:10.1002/fld.1834

Cited by 14 publications

(11 citation statements)

References 24 publications

(38 reference statements)

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“…Moreover, they made clear that there are at least two causes of the shock anomalies: one of these is a one-dimensional (1D) effect and the other is MD. The former appeared to be alleviated by adding (1D) dissipation to the shock-normal direction; whereas the latter could usually be suppressed by MD dissipation in the shock-perpendicular (transverse) direction [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

2012

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Hypersonic flow computations have proved to be very troublesome due to the appearance of shock anomalies (instabilities and oscillations), such as carbuncle phenomenon. These anomalies are categorized into one-dimensional (1D) and multidimensional (MD) modes, and these modes both arise from many factors and their combinations. Accurate prediction of hypersonic heating, a key issue in hypersonic flow computations, is therefore challenging especially for three dimensions (3D). In the present study, we focus on 3D shock anomalies and heating motivated by the following reasons: 1) Intuitively, MD shock anomalies are considered to develop more likely in 3D than in two dimensions (2D), but it cannot be proved mathematically, nor has it been numerically demonstrated; specifically, it is not clear yet whether the third dimension plays another role which is absent in 2D. 2) Most of proposed remedies for MD anomalies had been tested in 1D or 2D setups in the literature, but it is not guaranteed whether such MD dissipations actually work well in 3D. 3) It is already known to be troublesome to extend some of MD methods developed in 2D considerations to 3D. The numerical results show that 3D anomalies are too complicated to be predicted from their 2D counterparts, and that they can either be partly removed or (even worse) enhanced by MD dissipations. Therefore, robustness of a numerical method which worked well in 2D may not be preserved in 3D.  = thermal conductivity, = c p /Pr  = molecular viscosity Subscripts cell = value based on the minimum grid spacing F-R = Fay-Riddell's predicted value w = value on the wall  = freestream value 0 = stagnation value

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Section: Introductionmentioning

confidence: 99%

Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

2012

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“…And the grid at the mid-channel is perturbed alternatively at odd and even points with a small magnitude of ±10 −6 . For the Roe's FDS and the HLLC schemes, this grid is perturbed sufficiently to cause numerical instabilities so-called carbuncle phenomenon [6,7,10]. Figure 1 shows density contours at the three different positions…”

Section: Mach 6 Shock Moving Toward a Ductmentioning

confidence: 99%

A parameter-free AUSM-based scheme for healing carbuncle phenomenon

Phongthanapanich

2015

J Braz. Soc. Mech. Sci. Eng.

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“…Unfortunately, these schemes have some weaknesses and may produce numerical instabilities—including the sonic glitch, carbuncle phenomenon, and spurious oscillation—for certain problems, especially in hypersonic flow simulations 7‐9 . The sonic glitch phenomenon may arise when using the original Roe scheme in the presence of sonic rarefaction waves due to a disparity in wave speeds across the sonic point 10‐12 . A drawback of the Roe scheme is that it has to choose between normal compression shocks and expansion shocks.…”

Section: Introductionmentioning

confidence: 99%

“…The grid alignment and high grid aspect ratio usually influence the carbuncle phenomenon. Very elongated grids normal to the shock may enhance numerical instabilities leading to the anomaly 9,11,12 . Robinet et al 14 concluded that the carbuncle phenomenon was a pure numerical mechanism, so it should happen on certain unstructured grids.…”

Section: Introductionmentioning

confidence: 99%

A stable hybrid Roe scheme on triangular grids

Phongthanapanich

2020

Numerical Methods in Fluids

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Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to nonentropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This article proposes a simple, robust, and accurate hybrid Roe scheme (Roe+ scheme) by hybridizing the Roe scheme and the modified AUSMV+ scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd–even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

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Healing of shock instability for Roe's flux‐difference splitting scheme on triangular meshes

Cited by 14 publications

References 24 publications

Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

A parameter-free AUSM-based scheme for healing carbuncle phenomenon

A stable hybrid Roe scheme on triangular grids

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