A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John

doi:10.1016/j.jcp.2016.04.032

Cited by 6 publications

(19 citation statements)

References 40 publications

(53 reference statements)

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“…The largest percent difference is located near the edge of the boundary layer and is less than 1%. These results coincide with [21] where solutions between body-fitted and cut-cell methods for a hyperbolic tangent roughness also showed no visible differences. Overall, the comparison between the body-fitted and the cut-cell solutions is quite good.…”

Section: Cut-cell Methods Validationsupporting

confidence: 86%

“…The cut-cell method follows that of [9] and the finite-difference stencils used in the cut-cell method follow that of [21]. A schematic of the cut-cell grid is shown in Fig.…”

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

“…The closest twenty one points by index were used to determine the coefficients. This same method was used in [21] where it was found that a least-squares polynomial was more stable than a two-dimensional polynomial interpolation without a least-squares approximation. Irregular points are points near the roughness element where the standard finite difference grid stencil cannot be used due to an overlap of the stencil with the body.…”

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

“…(25), the viscous flux may be found and the corresponding coefficients are given in Table 2. It was shown in [21] that a solution procedure using the coefficients in Tables 1 and 2 along with a fifth-order interior scheme resulted in a fourth order method.…”

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

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Numerical Simulation of Hypersonic Boundary-Layer Instability in a Real Gas with Two-Dimensional Surface Roughness

Mortensen

Zhong

2015

45th AIAA Fluid Dynamics Conference

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Experimental and numerical results have shown that two-dimensional surface roughness can stabilize a hypersonic boundary layer dominated by second-mode instability. It is sought to understand how this physical phenomenon extends from an airflow under a perfect gas assumption to that of a real gas. To these ends, a new high-order shock-fitting method that includes thermochemical nonequilibrium and a cut-cell method to handle complex geometries unsuitable for structured body-fitted grids is presented. The new method is designed specifically for direct numerical simulation of hypersonic boundarylayer transition in a hypersonic real-gas flow with arbitrary shaped surface roughness. The new method is validated and shown to perform comparably to a high-order method with a body-fitted grid. For a Mach 10 flow over a flat plate with a real-gas model, a two-dimensional roughness element was found to stabilize the second mode when placed downstream of the synchronization location which is consistent with previous research for perfect-gas flows. For a Mach 15 flow over a flat plate, a two-dimensional surface roughness element stabilizes the second-mode instability more effectively in a real gas than in a perfect gas. Nomenclature −α i Growth rate c r Phase velocity c s Mass fraction of species s e v,s Species specific vibration energy, J/kg h Roughness height, m h o s Species heat of formation, J/kg M s Species molecular weight, kg/mol p Pressure, N/m 2 Q T −V,s Species vibration energy transfer rate, J/m 3 •s R Universal gas constant, 8.3143 J/mol• K T Translation-rotation temperature, K t Time, s T V Vibration temperature, K u j Velocity in jth direction, m/s nms Number of molecular species ns Number of species Subscripts ∞ Freestream b Blowing/suction slot s Species w Wall Symbols δ Boundary layer thickness, m δ ij Kronecker delta µ Viscosity, kg/m•s ω s Rate of species production, kg/m 3 •s ρ Density, kg/m 3

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Section: Cut-cell Methods Validationsupporting

confidence: 86%

“…The cut-cell method follows that of [9] and the finite-difference stencils used in the cut-cell method follow that of [21]. A schematic of the cut-cell grid is shown in Fig.…”

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

Section: B Cut-cell Numerical Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Simulation of Hypersonic Boundary-Layer Instability in a Real Gas with Two-Dimensional Surface Roughness

Mortensen

Zhong

2015

45th AIAA Fluid Dynamics Conference

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“…8. These oscillations are likely caused by the increased complexity of this 2D test case, which often leads to this behavior in high-order multi-stage schemes when compared to simpler flows such as the 1D test case [24]. One major difference is the fact that error measurements are not taken directly from the simulated data, but are instead based on frequencies and temporal growth rates calculated from the simulated data.…”

Section: Verification Of Higher-order Methodsmentioning

confidence: 99%

Low Mach preconditioned density-based methods with implicit Runge–Kutta schemes in physical-time

Alves

Santos

Falcão³

2021

J Braz. Soc. Mech. Sci. Eng.

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As far as the authors are aware, low Mach preconditioned density-based methods found in the peer-reviewed literature only employ multi-step schemes for physical-time integration. This essentially limits the maximum achievable temporal accuracyorder of these methods to two, since the multi-step schemes of order higher than two are conditionally stable. However, the present paper shows how these methods can employ multi-stage schemes in physical-time using the same low Mach preconditioning techniques developed over the past few decades. In doing so, it opens up the rich field of Runge-Kutta time integration schemes to low Mach preconditioned density-based methods. One and two-dimensional test cases are used to demonstrate the capabilities of this novel approach. The former simulates the propagation of marginally stable entropy perturbations superposed on a uniform flow whereas the latter simulates the temporal growth of vorticity perturbations superposed on an absolutely unstable planar mixing-layer. A novel procedure is employed to generate highly accurate initial conditions for the two-dimensional test case, it minimizes receptivity regions as well as deleterious interactions with artificial boundary conditions due to the numerical error introduced by approximate initial conditions. These test cases show that second, third and fourth order multi-stage schemes with strong linear numerical stability can be successfully utilized for the physical-time integration of low Mach preconditioned density-based methods.

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Optimal two-dimensional roughness for transition delay in high-speed boundary layer

Jahanbakhshi,

Zaki

2023

J. Fluid Mech.

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The influence of surface roughness on transition to turbulence in a Mach 4.5 boundary layer is studied using direct numerical simulations. Transition is initiated by the nonlinearly most dangerous inflow disturbance, which causes the earliest possible breakdown on a flat plate for the prescribed inflow energy and Mach number. This disturbance primarily comprises two normal second-mode instability waves and an oblique first mode. When localized roughness is introduced, its shape and location relative to the synchronization points of the inflow waves are confirmed to have a clear impact on the amplification of the second-mode instabilities. The change in modal amplification coincides with the change in the height of the near-wall region where the instability wave speed is supersonic relative to the mean flow; the net effect of a protruding roughness is destabilizing when placed upstream of the synchronization point and stabilizing when placed downstream. Assessment of the effect of the roughness location is followed by an optimization of the roughness height, abruptness and width with the objective of achieving maximum transition delay. The optimization is performed using an ensemble-variational (EnVar) approach, while the location of the roughness is fixed upstream of the synchronization points of the two second-mode waves. The optimal roughness disrupts the phase of the near-wall pressure waves, suppresses the amplification of the primary instability waves and mitigates the nonlinear interactions that lead to breakdown to turbulence. The outcome is a sustained non-turbulent flow throughout the computational domain.

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A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

Cited by 6 publications

References 40 publications

Numerical Simulation of Hypersonic Boundary-Layer Instability in a Real Gas with Two-Dimensional Surface Roughness

Numerical Simulation of Hypersonic Boundary-Layer Instability in a Real Gas with Two-Dimensional Surface Roughness

Low Mach preconditioned density-based methods with implicit Runge–Kutta schemes in physical-time

Optimal two-dimensional roughness for transition delay in high-speed boundary layer

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