Vortex Interactions with a Jet in a Supersonic

Crossflow

Luca Maddalena∗ and Joseph A. Schetz†

Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0203, USA

Reece Neel‡

AeroSoft Inc., Blackburg, VA, 24060, USA

This paper is concerned with the interaction of the usual vortex structure producedby jet injection into a supersonic crossflow and an additional axial vortex typical of thosethat might be produced by the inlet of a scramjet or the forebody of a vehicle to becontrolled by jet interaction phenomena. A combination of experiments, computationalfluid dynamics and vortex dynamics analysis is used to study this flow. The cases treatedare for sonic, heated helium injection from a circular jet inclined at 30 degrees to a Mach4 flow at high Reynolds number conditions. The additional axial vortices are generated bya strut-mounted, diamond cross-section wing mounted upstream of the injection location.The results document the large influence that the additional axial vortices have on thebasic jet flow development. The plume were severely distorted, penetration was affectedand mixing was altered.

Nomenclature

M Mach numberq Jet-to-freestream momentum ratioΓ Circulationu Flow velocityα Helium mass fractiond Diameterdeff Effective diameterφ Potentialρ DensityCd Discharge coefficientτ Swirl anglex Axial distance downstream of the injection pointy Lateral distance from the injection pointz Vertical distance from the tunnel wall

Subscriptj Jet exit property∞ Free-stream propertyx Component in the x directiony Component in the y directionz Component in the z direction

∗Graduate Research Assistant, presently Postdoctoral Scholar, Graduate Aeronautical Laboratories, California Institute ofTechnology, AIAA Member.

†Holder of the Fred D. Durham Chair, Aerospace and Ocean Engineering Department, and AIAA Fellow.‡Research Engineer, AIAA Member.

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46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-762

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I. Introduction

There are a number of applications of jet injection into a supersonic crossflow where additional vorticesare present in the approach flow. First, hypersonic airbreathing flight vehicles, such as the scramjet, arecharacterized by extremely small flow residence times in the engine that hinder the fuel/air mixing process.Vorticity generation plays a key role in all turbulent mixing processes, and fuel jets injected across anairstream are known to produce pairs of strong axial vortices.1,2 The behavior of thiese vortical structuresare then an important factor in the design and in the subsequent operation of a scramjet vehicle throughoutits flight envelope. However, the inlets and other features of these vehicles can induce vortical flows enteringthe combustor from corners and other areas. Second, jet interaction flows are important for supersonic andhypersonic vehicle control, and one can expect vortical structures produced by the forebody or other vehiclefeatures. Here, we are interested in the interaction between the vortex system in the jet plume and theseadditional vortices. Many experiments have been performed in the field of injection and mixing in supersonicflow. The subject of transverse injection of a gas into a supersonic main flow has been studied extensively.3–6

An extensive review of injector mixing characteristic is given in Schetz et al.7

There have been many studies of the vortex structures in the plumes of jets, however they have beenconfined mostly to the lower speed range leaving vortices in supersonic flow relatively unexplored (Smart etal.,8,9 Milanovic,10 Naughton,11 Levey12 and Maddalena et al.13).

The aim of the present work is to examine some features of the interaction between an axial vortex anda transverse jet of a light gas in a Mach 4 crossflow. Particle Image Velocimetry (PIV) and Planar LaserInduced Fluorescence (PLIF) are known to be sensitive to steep velocity gradients. Earlier workers had triedto use PIV and PLIF to measure the velocities in the cross-plane of a supersonic vortex but the uncertaintiesfor these quantities are large. To accomplish our task, a five-hole conical probe was used for obtainingtotal pressure, Mach number and flow angle data. A combination of experiments, Vortex Dynamics andComputational Fluid Dynamics (CFD) was used in this study.

II. Vortex Dynamics Considerations

The behavior of the counter-rotating vortex pair created in the plumes of jets in a crossflow is a keyfeature of fuel injection and mixing in scramjets and other jet interaction applications. It is, therefore, ofinterest to understand how additional vortex structures might interact with the vortices in the jet plume.Concepts of vortex dynamics were used to conduct some preliminary studies for idealized cases. The 3D,steady case was represented using an analogy with the 2D, unsteady case. Marble14 suggested this sameanalogy in a different, but related situation. Let’s consider a lifting line of length equal to 2, placed alongthe y-axis in the z=0 plane, from y = -1 to y = 1 ( Figure 1)

Figure 1: The horseshoe vortex in supersonic flow

It is possible to show that the potential of the lifting line can be expressed in the form

φ =Γ2π

tan−1 x (y − 1)z√

Ω(1)

where Γ is the circulation and Ω defined as: Ω = x2−(√

M2 − 1)2[(y − 1)2 + z2

]. The potential is other than

zero only within the two Mach cones arising at the end of the lifting line, while it is zero in the remaining

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space. The velocity components corresponding to the potential can be easily found. If, for example, weconsider the component w in the z direction we obtain:

w =∂φ

∂z=

Γπ

x(y − 1)(Ω− (M2 − 1)z2

π[z2Ω + (y − 1)2 x2

]√Ω

(2)

The important observation is that near the axis of the vortex the velocity components are the same as inEquation 2 and they behave exactly as in the zone near a vortex filament in incompressible flow. Therefore,the induced velocity in zones far behind a vortex generator ( exactly at x = ∞ or in the case of the 2Danalogy suggested by Marble14) can be determined with the equation of Biot-Savart for incompressible flow(Ferri15).

Consider a simple case where an axial vortex passes close to the side of the plume from the jet. The jetplume can be idealized as a pair of counter-rotating axial vortices, and the strength of these vortices wascalculated after a complete five-hole probe survey. The equations of motion for N interacting point vorticesin the bounded plane (y-z) consists of 4N first order, nonlinear, ordinary differential equations. To gainan understanding of the possible effect of these streamwise vortex interactions, several simple simulationwere studied. The main result is that the presence of an axial vortex of sufficient strength (same order ofmagnitude of the vortices in the CVP) and sense can have a large effect on jet penetration. In addition, theplume can be distorted, which will affect mixing. Based on these results, a vortex generator was designed toproduce a tip vortex of a strength comparable to that of one of the typical CVP found in the plume of a jetin a crossflow (Γ = 1.9m/s2)13

III. Test Arrangement

All wind tunnel tests were performed at a nominal free-stream Mach number of 4.0 as shown in Figure 2.Free stream conditions were fixed at a total pressure of 1034 kPa with an ambient mean total temperatureof approximately 295 K, producing a freestream Reynolds number of 5.77 · 107 per meter. These conditionsresulted in a turbulent boundary layer with a thickness of approximately 20 mm at the point of injection.A weak shock at the junction of the tunnel nozzle and the test section plate resulted in a Mach number of3.8 at the injection station.

The circular injector was transversely angled 30 deg. relative to the downstream direction on the testsection floor and had a diameter of 3.23mm. Heated helium was used as the injectant to simulate hydrogenfuel. The injectant was heated to an average total temperature of 313K, and the average injection Machnumber was sonic. The jet-to-freestream momentum flux ratio, q, was set to 2.1. Recall that q is defined by

q =

(ρu2

)j

(ρu2)∞(3)

For the present configuration, the corresponding helium flow rate was 3.4 g/s.A Cartesian coordinate system was chosen with the origin on the wall surface along the test section

centerline, as shown in Figure 2.

Figure 2: Tunnel arrangement and coordinate system

The origin of the coordinate system is located on the wall in the middle of the injector. The positivex-axis is in the free stream direction, the positive z-axis is in the vertical direction perpendicular to the wall,

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and the y-axis spans the test section. The five-hole probe was situated with its tip at 16deff downstream ofthe injection point and was able to traverse in the vertical and horizontal direction in increments as smallas 0.5mm. The effective diameter, deff , is defined as:

deff = C0.5d d (4)

where Cd is the injector discharge coefficient. The measured injector discharge coefficients was 0.88.

(a) Vortex generator and concentration probe (b) Conical five hole probe used for the vortexsurvey

Figure 3: Test section arrangement

Figure 4: Wing tip position. The adopted reference system

The experimental arrangement is shown in Figure 3(a) and Figure 3(b). The vortex generator was arectangular half wing with a diamond shaped cross section (6 degrees half angle), a chord length of 2 in,and span of 3.5 in. It was located 2 chords upstream of the injector center. The convention adopted forspecifying the location of the wing tip with respect to the injection point is shown in Figure 4.

IV. Instrumentation

Flowfield and vorticiy measurements were made using a miniature, five-hole pressure probe, a diffuserthermocouple and a species composition measurement probe.16

IV.A. The Conical Five-hole probe

A customized L-shaped five-hole probe from Aeroprobe Inc., was utilized to measure the vortical flow pat-terns. The probe used in the present investigation is depicted in Figure 3(b) and the details of the tip areshown in the schematic in Figure 5. An extensive review on the theory and operation of the probe is givenin Maddalena et al.13

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Figure 5: Detail of conical five-hole tip (all dimensions are in inches)

The cone angle is machined to a high order of accuracy. The probe uses piezoresistive Endevco miniaturetransducers ( Model 8507-C-50) chosen for their smaller size, large temperature-compensation range, fasttime-response, and high sensitivity. The probe has a 99% time-response to a step input of 11 milliseconds.

IV.B. Species Composition

Species composition measurements were obtained using an integrated sampling probe and gas analyzerdesigned specifically for use in supersonic flow. The fundamental concepts and design of this probe weredeveloped at Virginia Tech by Prof. W. Ng and his students.17 The concentration probe is an aspiratingtype attached to a vacuum pump. The unit consists of a constant temperature hot-film sensor operating ina channel with a choked exit. The hot film has a diameter of 50.8 µm and an active sensor length of 1.02mm. The inlet hole at the tip of the probe has the same diameter as the choked orifice, d=0.63 mm. Thesediameters are chosen so as to preclude the occurrence of a standoff shock at the probe tip. Flow visualizationfrom spark schlieren verified this design intention. The probe is designed with a diverging channel betweenthe tip and the sensor plane. The internal probe diameter diverged from 0.63 mm at the inlet to 3.8 mm atthe sensor plane, causing a normal shock to occur inside the probe in the diverging channel. In this fashion,a stream tube equal in area to the probe capture area can enter the probe undisturbed.

IV.C. Probe Traversing System

This system consisted of two Velmex, Inc. UniSlide Assemblies linear traverses mounted to each other,operated by 200-steps per revolution Warner Electric stepping motors. This enabled movement in thedownstream and vertical directions. The two traverses were operated by a Velmex, Inc. stepping motorcontroller, which was in turn operated by the PC via LabView.

IV.D. Data Acquisition

General data acquisition was performed with a personal computer running with a Windows operating systemand a 16-bit, 16-channel single-ended A/D converter made by National Instruments, Model AT- MIO-16XE-50. To reduce signal noise, the A/D converter was used in an 8-channel differential input mode. Theconverter was configured with a National Instruments, Model AMUX-64T multiplexer board to increase thetotal number of usable differential channels to 32. The multiplexer was also equipped with an onboard coldjunction compensator for temperature measurement. To minimize signal noise, the multiplexer was placedin a metal box, which was grounded to a copper water pipe in the room. The data acquisition system usedLabVIEW software to process and record the input signals. During an experiment, the input signals weresampled at a rate of 500 Hz.

IV.E. Uncertainty Estimates of Flow Properties

Typical values and uncertainty estimates for the flow properties calculated using the five-hole probe are listedin Table 1. The values of and uncertainties in the Mach number M, the total pressure, the static pressure,and the Mach number components Mx, My, and Mz are presented. The uncertainty estimates listed in Table1 are representative of all measurements performed for the work.

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Table 1: Estimated five-hole probe uncertainties

Total pressure, % Static presure, % Mx% My% Mz%

4 3 2 2 4

For the concentration probe, the uncertainty is estimated to be 7% in terms of mass fraction. Thisestimation was determined based on the results of a jitter program in which a 2% error in the molar fractionwas assumed.

V. Experimental Results

Some comparisons of the flow with axial vortices interacting with the jet plume in various locations areconsidered. First, the details of the isolated vortex without jet injection are presented.

V.A. Vortex Survey

The main objective of the vortex characterization was to determine the Mach number, total pressure, andswirl distributions in the core region of the supersonic wing tip vortex. A shadowgraph of the flow in whichit is possible to identify the vortex is presented in Figure 6.

Figure 6: Shadowgraph of the wing tip vortex

The survey of the tip vortex was conducted at a station located 16deff downstream of the injector. Theposition of the vortex is defined as the position at which the Pitot pressure was observed to be a minimum.Spanwise Pitot pressure distributions of the region of the tip vortex are shown in Figure 7 indicating thatthe tip vortex is a region of significant deficit in total pressure. The total pressure distributions reach aminimum at approximately 7mm.

Figure 7: Pitot pressure distributions used to locate the vortex

Figures 8(a) to 8(c) show the Mach number distributions. For the geometry of the current experiments,Mx may be interpreted as swirl component of the Mach number. The distribution shows a similarity to

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(a) Swirl Mach number (b) Spanwise Mach number

(c) Streamwise Mach number (d) Swirl Mach number

Figure 8: Measured Mach number components in the isolated vortex

the work of Smart8 with an inner linear swirl distribution, surrounded by a region with swirl similar to anirrotational vortex. The point with zero swirl corresponds with the vortex axis. It is noted, however, that theprofile is not symmetric but shows a larger swirl outboard of the half-wing . This asymmetry is also typicalof low-speed flow wing tip vortices. The average core diameter was observed to be of 4mm. Figure 8(b)shows the spanwise component of the Mach number My. In order to interpret the observed distribution, itis worth noting that this shows the radial Mach number component in the vortex core in combination withthe wake.

Figure 8(c) shows the distribution of the streamwise Mach number. A significant Mach number deficitis observed to occur in a small region near the axis of the vortex. The wake-like profile reaches a minimumof M = 1.77. Again, the wake-like streamwise Mach number distribution observed in this experiment issimilar to those found in Milanovic10 and Smart9 and is attributed to the momentum deficit in the wing’sboundary layer. Streamwise Mach number deficits of this magnitude have important implications for thevortex interaction studies. Based on the results presented above, the magnitude of the swirl angle, τ , is plot-ted in Figure 8(d). As noted earlier, the vortex is not symmetric, leading to a peak swirl angle of 10.5 degrees.

V.B. Mass Fraction Contours

Here, we present the change in the jet plume produced by impingement of the additional axial vortexat different locations, as defined in Figure 4. The main results are for injectant concentration. Helium

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concentration data is presented in the form of mass fraction contours. Consider first the case in Figure 9(a)where the tip of the vortex is at x = 2deff and h = 1deff . The core of the jet, defined as the maximumhelium mass fraction, is located at approximately y/deff = 1 at an elevation of z/deff = 2.5. The maximumconcentration is αmax = 0.76. The plume width extends for 9deff . From the picture, it is clear thatthere is a tremendous distortion of the counter-rotating vortex pair (CVP) that, in absence of the wing tipvortex, usually manifests itself with the classic horse-shoe shape. In Figure 9(b), in which the tip of thevortex generator is located at x = 4deff and h = 1deff shows a lower penetration than the previous case.The plume is shifted in the left direction, and it appears that the CVP formation, even if inhibited by theadditional vortex, occurs.

(a) case x=2 deff and h= 1 deff (b) case x = 4deff and h= 1 deff

(c) case x=0 deff and h= 2 deff (d) case x=0 deff and h= 1 deff

Figure 9: Mass fraction contours

The maximum concentration, αmax = 0.74, is found at an elevation of z/deff = 2.1. Figure 9(c) andFigure 9(d) show the effects of the tip of the vortex generator at x = 0 with h = 2deff and h = 1deff .The maximum concentrations are αmax = 0.81 and αmax = 0.84, respectively. The small variation in theposition of the wing results in a completely different morphology of the mass fraction distribution. In fact,in Figure 9(a) there is an entrainment effect and in Figure 9(d) we can identify a partial rotation of theplume, with the same sense of the circulation of the vortex, which results in the lifting of the right side.

V.C. The complete flowfield

A complete conical probe survey was obtained for the case with the tip of the vortex generator at x = 2deff ,h = 1deff selected as an interesting case. The results are shown in Figure 10. The noteworthy feature is the

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entrainment process, driven by the wing tip vortex that occurs in the left side of the concentration contoursin Figure 11. Figure 10 shows that the strong influence of the wing tip vortex results in an inhibition ofthe right side of the CVP and a reduction of the strength of the left component compared with the baselinecase. This can help to explain the fact that the maximum concentration in the plume is almost twice thebase case without a vortex.16

Figure 10: The complete CVP and wing tip vortex interaction flowfield

Figure 11: Mass fraction contours for the case x=2 deff and h= 1 deff

VI. Computational Methods and Results

The CFD simulations were performed using the GASP Version 4.3 flow solver.18 GASP is a time-dependent, three-dimensional, Reynolds-averaged Navier-Stokes (RANS) solver. It solves the integral formof the governing equations using an upwind-based, finite volume formulation. Two simulations were per-formed for comparison with the experimental data. The first simulation involved the single circular injectorinteracting with the freestream flow. The second simulation modeled the injector along with an axial vortex.The mesh used in these simulations consisted of 6 million cells with 14 blocks. The grid was clustered inthe near-wall regions in order to capture the boundary layer and had an initial wall spacing which gave ay+ of less than 1. Because of the asymmetry of the flow, the entire jet interaction was modeled. For thesolid walls, the no-slip adiabatic boundary condition was used. The side and outflow surfaces used a firstorder extrapolation condition. The injector was modeled down into the wall about four jet diameters andhad sonic flow conditions for helium applied. The inflow surface used pointwise conditions to describe both

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the boundary layer and axial vortex. The boundary layer height at the inflow was determined from theexperimental data and used to create the inflow profile. For the case with the axial vortex, the vortex wassuperimposed onto the boundary layer profile in order to produce the inflow pointwise data. The equationsused to describe the vortex came from Jiang et al.19 From the experiment, velocity profiles were takenat 16x/deff downstream from the center of the injector. This was done with the injector off in order todetermine the strength of the axial vortex at the downstream location. Using this downstream data, theinflow settings for the vortex were adjusted to give the best correlation with the experimental data. The Mx

and Mz data profiles comparing the CFD with the experiment for the axial vortex case with no injection aregiven in Figure 12

(a) Mx profiles (b) Mz profiles

Figure 12: The Mx and Mz data profiles comparing the CFD with the experiment for the axial vortexwith no injection

Over half of the vortex is immersed within the boundary layer, which made predicting the inflow vortexprofile even more difficult. Therefore, the uncertainties associated with the inflow conditions were larger forthe simulation involving the axial vortex, and that should be kept in mind when correlating the CFD resultswith the experimental data. Another alternative would have been to model the vortex generator itself, butthis was beyond the scope of this work.

Several turbulence models were considered for these simulations which included the Wilcox 1998 k − ωmodel, the Spalart-Allmaras (S-A) model,20 and the Reynolds Stress model (RSM) by Wilcox.21 The RSMwas selected for use in the simulations because it did a better job of modeling the axial vortex. Both the othertwo turbulence models greatly reduced the vortex strength (by over 60%) by the time it got to 16x/deff .While some of its strength would be dissipated due to the influence of the boundary layer, what was observedwith the k − ω and S-A models appeared to be a deficiency in the models themselves. Therefore, the RSMwas used for both simulations presented here.

A complete conical probe survey was obtained for the case with the tip of the vortex generator atx = 2deff , h = 1deff selected as an interesting case. The numerical analysis presented here refers to thisspecific case.

The helium concentration profiles for the case without the axial vortex are shown in Figure 13(a). In thisfigure the He concentrations are overlaid with in-plane streamlines. The streamlines help show the counterrotating vorticies more clearly, as well as the vortex cores. A similar plot is shown in Figure 13(b)for the casewith the axial vortex. The effect of the axial vortex is clearly seen in that it stretches and pushes up the leftcounter rotating vortex. The peak concentration for this case at 16deff is 0.797 while for the case with noaxial vortex it was 0.785. So the peak concentrations were about the same. The evolution of the analogouscase at 30deff is shown in Figure 14(a) and Figure 14(b). The analysis of this downstream evolution showsthat an important entrainment driven by an axial vortex occurs and results in a higher penetration with awider jet plume compared to the case without a vortex. Figure 15 shows a number of streamlines beginningfrom the injector. This plot also shows the pressure on the plate surface. The streamlines are colored tomass concentration and have the same scale as in Figure 13.

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(a) Case without the axial vortex (b) Case with the axial vortex

Figure 13: Predicted helium concentration profiles at x/deff = 16

(a) Case without the axial vortex (b) Case with the axial vortex

Figure 14: Predicted helium concentration profiles at x/deff = 30

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Figure 15: Streamlines from the injector and pressure on the plate surface

VII. Conclusions

A study of the interaction of the usual vortex structure produced by jet injection into a supersonic cross-flow and an additional axial vortex typical of those that might be produced by the inlet of a scramjet orthe forebody of a vehicle to be controlled by jet interaction phenomena was presented. A combination ofexperiments, computational fluid dynamics and vortex dynamics analysis was used to study this flow. Thecases treated were for sonic, heated Helium injection from a circular jet inclined at 30 degrees to a Mach 4flow at high Reynolds number conditions. The additional axial vortices were generated by a strut-mounted,diamond cross-section wing mounted upstream of the injection location. The results document the verylarge influence that the external axial vortices have on the basic jet flow development. The main conclusionsdrawn from these studies are as follows:

1) The generated wing tip vortex has a circulation of Γ = 1.6m2/s and a maximum swirl angle of 10.5degrees. These were the values we were planning to investigate.

2) A wake-like streamwise Mach number distribution was observed, but the vortex was able to sustainthe bow shock generated by the injection in the supersonic stream. It is well known that a wake-like profiledecreases the critical Mach number at which vortex bursting occurs

3) The results show a higher value of the helium maximum concentration in all the cases investigatedwith an addition of an axial vortex, accompanied by a profound influence in the jet’s plume morphology.

4)The flow field survey shows that an incoming axial vortex can dramatically influence the formation ofthe usual jet counter-rotating vortex pair (CVP), resulting in an asymmetry.

5)The combined flow field survey and concentration measurements show that an important entrainmentdriven by an axial vortex occurs and results in a higher penetration with a wider jet plume compared to thecase without a vortex.

6) The experimental fact that in the measurement plane the maximum helium mass fraction is higherthan the baseline case doesn’t define much about the further downstream development. The dynamics andconsequently the mixing might accelerate once the reorganization of the vortical flow is completed.

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7) The CFD results are qualitatively in agreement with the physics of the vortex interactions predicted bythe vortex dynamics analysis and with the experimental results. The discrepancy in the quantitative results(concentration levels) appear to be related to the turbulence model. In this study, the RSM was selectedfor use in the simulations because it performed better in modeling the axial vortex. Both the other twoturbulence models (k-ω and S-A) greatly reduced the vortex strength (by over 60%) by the time it reached16x/deff . While some of its strength would be dissipated due to the influence of the boundary layer, whatwas observed with the k-ω and S-A models appeared to be a deficiency in the model themselves. Due to thewell established importance of vortical flow for the mixing in jets in a supersonic crossflow, the tremendousdifferences in the dissipation of the vortex strength depending of the adopted turbulence models, as reportedin this work, deserve further investigation.

Acknowledgments

This research was supported by the Air Force office of Scientific Research under a MURI lead by PaulDimotakis at Caltech.

References

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AIAA Paper 89-2459, July 1989.18“GASP 4.0 User Manual”, AeroSoft, 2002, ISBN 09652780-5-0.19Jiang, G.S. and Shu, C.W. “Efficient Implementation of Weighted ENO Schemes”. Journal of Computational Phyics,

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