High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

Yee, H. C.; Klopfer, G. H.; Montagne, J. L.

doi:10.1016/0021-9991(90)90241-r

Cited by 138 publications

(64 citation statements)

References 22 publications

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“…To resolve stability problem linear numerical dissipation or artificial viscosity is added into classical shock-capturing methods (H. C. Yee, 1989) (H. C. Yee, 1987) (H. C. Yee, 1988 (Boulahia .A, 2014).In 1983, Harten (Harten A. , 1983) introduced the concept of Total Variation Diminishing (TVD) scheme. TVD schemes are monotonicity preserving schemes and therefore, it must not create local extrema and the value of an existing local minimum must be non-decreasing and that of a local maximum must be non-increasing.…”

Section: Nomenclaturementioning

confidence: 99%

To Study Large Time Step High Resolution Low Dissipative Schemes for Hyperbolic Conservation Laws

Siddiqui

Hussain

Baig

2016

JAFM

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Total Variation Diminishing (TVD) schemes are low dissipative and high resolution schemes but bounded by stability criterion CFL<1 for explicit formulation. Stability criteria for explicit formulation limits time stepping and thus increase computational cost (computational time, machine cost). Research in the field of large time step (LTS) scheme is an active field for last three decades. In present work, Zhan Sen Qian's modified form of Harten LTS TVD scheme is studied and used to solve one dimensional benchmark test cases. SOD and LAX cases of shock tube problem are solved to understand the behavior of modified large time step scheme in regions of discontinuities and strong shock waves. The numerical results are found to be in good agreement with analytical results, except slight oscillations near contact discontinuity for larger values of K. Results also reveal that the discrepancy between numerical and analytical results near expansion fan, contact discontinuity and shock grows for larger values of K. Increase in discrepancy is due to the increase in truncation error. Truncation error strongly depends on step size and step size increases as CFL (or K) increases. In present work, the correction into the numerical formulation of characteristic transformation is discussed and the inverse characteristic transformations are performed using local right eigen vector in each cell interface location. This idea of extending Harten's large time step method for hyperbolic conservation laws proved to be very useful as the results shows that the modified scheme is a high resolution low dissipative and efficient scheme for 1D test cases.

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Section: Nomenclaturementioning

confidence: 99%

To Study Large Time Step High Resolution Low Dissipative Schemes for Hyperbolic Conservation Laws

Siddiqui

Hussain

Baig

2016

JAFM

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“…1 (left), for instance, shows the carbuncle problem generally appears when an upwind scheme is used. Entropy correction with a tunable parameter is introduced to the TVD scheme [29] which can eliminate the carbuncle phenomenon. However, the aforementioned DCD scheme is proved to be free of instability without any case-by-case tunable parameter as shown in Fig.…”

Section: The Original Dcd Scheme For Multi-component Systemmentioning

confidence: 99%

On the numerical technique for the simulation of hypervelocity test flows

Hu¹,

Wang²,

Jiang³

et al. 2015

Computers & Fluids

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a b s t r a c tA shock-expansion tube (SET) is one of the major ground test facilities to generate really high-enthalpy and hypervelocity test flows. However, the strong shock wave may give rise to chemically non-equilibrium characteristic flow feature in a SET. In addition, the test time duration of a SET is extremely short which leads to difficulties in measurements and flow diagnostics. It is therefore appropriate to consider employing CFD approach, coupled with available experimental data, to determine the characteristic of the test flow in a SET. The dispersion-controlled dissipative scheme (DCD) is used for our simulation of chemically non-equilibrium flows associated with a SET. In this paper, the several numerical issues which occur in the computational investigation of the test flow in our SET facility are discussed. A new flux splitting algorithm based on local characteristics is worked out for the DCD scheme to mitigate any spurious oscillations. With the mentioned updated DCD scheme, the computed results compare well with the experimental data provided for validation.

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“…All partial derivatives are discretized using second-order accurate, centered finite difference stencils except for the convection derivative, which is discretized using the approximate Riemann solver of Roe 31 and made second-order accurate through a symmetric minmod limiter by Yee et al 42 The discretized residual is solved to steady state using a block-implicit factorization …”

Section: Methodsmentioning

confidence: 99%

Numerically Simulated Comparative Performance of a Scramjet and Shcramjet at Mach 11

Chan

Sislian

Alexander

2010

Journal of Propulsion and Power

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This study investigates the design and aeropropulsive performance of a complete, hydrogen powered, shock-induced combustion ramjet (shcramjet) at a flight Mach number of 11 and altitude of 34.5 km. The design includes a Prandtl-Meyer compression inlet, cantilevered ramp fuel injectors, a shock-inducing wedge and a divergent nozzle. Numerical studies are undertaken using the WARP code that solves the three-dimensional Favre-averaged Navier-Stokes equations closed by the Wilcox k-ω turbulence model and the Jachimowski H 2 /air chemical kinetics model. Studies of fuel injection properties, mixing duct length, combustor wedge and nozzle geometry are completed to maximize the overall performance of the vehicle. The final shcramjet configuration generates a specific impulse of 1110 s. A comparison is undertaken with a scramjet vehicle at identical flight conditions and using many of the same components. The comparable scramjet generates a higher specific impulse of 1450 s although it is significantly larger and therefore heavier.ii

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High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

Cited by 138 publications

References 22 publications

To Study Large Time Step High Resolution Low Dissipative Schemes for Hyperbolic Conservation Laws

To Study Large Time Step High Resolution Low Dissipative Schemes for Hyperbolic Conservation Laws

On the numerical technique for the simulation of hypervelocity test flows

Numerically Simulated Comparative Performance of a Scramjet and Shcramjet at Mach 11

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