High-Order Shock-Fitting and Front-Tracking Methods for Numerical Simulation of Shock-Disturbance Interactions

Rawat, Pradeep Singh; Zhong, Xiaolin

doi:10.2514/6.2009-1138

Cited by 5 publications

(11 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have shown that the shock-fitting implementations that are uniformly high order accurate [30][31][32][33] and suffer no spurious oscillations around the shock as generally observed with shock capturing formulations. We have implemented these shock-fitting methods for shock and isotropic turbulence interaction problems.…”

Section: Achievementsmentioning

confidence: 54%

“…In our previous work we have developed and evaluated the shock-fitting methodology for canonical problems where flow disturbances interact with a strong shock [31,32] in one and two dimensional setups. It was observed that results from shock-fitting methods for such problems showed uniformly high-order convergence and did not incur any spurious numerical oscillations.…”

Section: Implementation Of Shock-fitting For Shock-turbulence Interacmentioning

confidence: 99%

See 1 more Smart Citation

Simulations of Turbulent Flows with Strong Shocks and Density Variations

Zhong¹

2012

Self Cite

View full text Add to dashboard Cite

Section: Achievementsmentioning

confidence: 54%

Section: Implementation Of Shock-fitting For Shock-turbulence Interacmentioning

confidence: 99%

Simulations of Turbulent Flows with Strong Shocks and Density Variations

Zhong¹

2012

Self Cite

View full text Add to dashboard Cite

“…Current work is continuation of our efforts presented in Refs. [1,2]. Here, underlying idea is to develop and use shock-fitting along with high order schemes to gain knowledge about nonlinear phenomena involving interaction of strong shocks and turbulent flows.…”

Section: Motivation and Scope Of Current Studymentioning

confidence: 99%

“…1. In our previous work [1,2], some simple canonical problems were considered by us and results obtained point to the highorder accuracy of the shock-fitting methods for such problems.…”

Section: Motivation and Scope Of Current Studymentioning

confidence: 99%

Numerical Simulation of Shock-Turbulence Interactions Using High-Order Shock-Fitting Algorithms

Rawat

Zhong

2010

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Self Cite

View full text Add to dashboard Cite

High-order methods are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. In our previous work [1, 2] we have shown that algorithms based on shock-fitting methodology can solve the flow with highorder accuracy near as well as away from the shocks without any numerical oscillations. In the current study, we extend the fifth order shock-fitting algorithm to carry out Direct Numerical Simulations (DNS) of interactions of shock waves with realistic isotropic turbulence. Incoming isotropic turbulence is developed in a temporal simulation of solenoidal fluctuations in a periodic box. Using Taylor's hypothesis these fluctuations are prescribed upstream of the shock wave and the flow behind the shock wave is computed using the shock fitting algorithm. In this paper we investigate interactions of isotropic turbulence with normal shock waves of Mach numbers 1 2.0 10.0 M and compare the results against numerical and Linear Interaction Analysis (LIA) results available in the literature. The results follow the trends observed in the previous studies which were only for the weak shocks. It is observed that velocity fluctuations are amplified across the shock wave and almost same amplification in turbulent kinetic energy observed for stronger than Mach 4 shocks. Transverse vorticity fluctuations are significantly increased across the shock and amplifications increase with increasing Mach number. Taylor microscales decrease as flow passes through a shock wave and amplification factor for transverse microscale agree well with the LIA results. Overall, the results generally confirm the findings by earlier numerical simulations and provide results for stronger shocks than those considered by numerical studies in the past. In future, higher Reynolds number flows will be considered with larger computer resources to avoid excessive viscous decay observed in the current study.

show abstract

“…High-order shock capturing schemes have been the methods of choice in most previous numerical simulation studies of shock turbulence interaction [1][2][3][4]. However, popular shockcapturing schemes reduce to first order accuracy near the shock due to the use of dissipation near the shock [5][6][7]. Moreover, spurious numerical oscillations have been observed when solving strong-shock and turbulence interaction problems with shock-capturing schemes [7,8].…”

Section: Introductionmentioning

confidence: 99%

Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

Rawat

Zhong

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Self Cite

View full text Add to dashboard Cite

Canonical problem of interaction of a normal shock and isotropic turbulence is fundamental to many important scientific and engineering applications. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. Since high order methods are critical for direct numerical simulation of turbulent flows, we use a shock-fitting method that has been shown to be fifth-order accurate near as well as away from the shock. Moreover, unlike shock-capturing schemes, there are no spurious oscillations even with very strong shock waves. We carry out Direct Numerical Simulation (DNS) of canonical shock-turbulence interaction problem for flows with mean Mach numbers ranging from 2 to 20 and turbulent Mach number varying from 0.12 to 0.38. A Reynolds number based on Taylor microscale, Re , of up to 40 is used, requiring more than 30 million grid points per simulation. Such high mean Mach number values have never been considered in past for study of shock turbulence interactions. Some new trends are observed in turbulent statistics as mean Mach number is increased. Maximum value of streamwise velocity fluctuations downstream of the shock is found to be initially decreasing as Mach number is increased but for stronger than Mach 8 shocks this trend reverses. Similarly maximum streamwise vorticity fluctuations in post-shock flow first increase and then decrease as mean Mach number is increased. We observe that vorticity fluctuations return to isotropy behind the shock for some cases. Increasing mean Mach number and Reynolds number leads to delay in the return to isotropy in the vorticity fluctuations. Overall, the results generally confirm the findings by earlier numerical simulations and provide new trends for stronger shocks than those considered by numerical studies in the past.

show abstract

High-Order Shock-Fitting and Front-Tracking Methods for Numerical Simulation of Shock-Disturbance Interactions

Cited by 5 publications

References 35 publications

Simulations of Turbulent Flows with Strong Shocks and Density Variations

Simulations of Turbulent Flows with Strong Shocks and Density Variations

Numerical Simulation of Shock-Turbulence Interactions Using High-Order Shock-Fitting Algorithms

Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

Contact Info

Product

Resources

About