Calculations of 3D compressible flows using an efficient low diffusion upwind scheme

Hu, Zongjun; Zha, Gecheng

doi:10.1002/fld.810

Cited by 17 publications

(11 citation statements)

References 17 publications

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“…FASIP has been intensively validated for various 2D and 3D steady and unsteady flows. FASIP has implemented advanced numerical algorithms including various approximate Riemann solvers [29,30,31], 3rd order MUSCL schemes, high order WENO schemes and central differencing schemes [32,33,34,35], non-reflective boundary conditions [36], implicit unfactored Gauss-Seidel dual time stepping for unsteady calculation [37,38], fluid-structural interaction [39,40,41], Reynolds averaged Navier-Stokes turbulence models [42,43], DES and LES [44,45,46,47], preconditioning for incompressible flows [48,35], and high scalability parallel computing [49]. For the sonic boom calculation in this paper, the Roe's approximate Riemann solver [50] with 3rd order MUSCL scheme [51] and Minmod limiter is used.…”

Section: Validation Of Sonic Boom Simulationmentioning

confidence: 99%

Toward Zero Sonic-Boom and High Efficiency Supersonic Flight, Part I: A Novel Concept of Supersonic Bi-Directional Flying Wing

Zha

Espinal

2010

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

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This paper introduces a novel concept for supersonic airplane: supersonic bi-directional (SBiDir) flying wing (FW) concept, which is to achieve low sonic boom, low supersonic wave drag, and high subsonic performance. The SBiDir-FW planform is symmetric about both longitudinal and span axes. For supersonic flight, the planform will have low aspect ratio and high sweep angle to minimize wave drag. For subsonic mode, the airplane will rotate 90 • and the sweep angle will be reduced and the aspect ratio will be increased. To minimize sonic boom, the pressure surface of the flying wing will employ an isentropic compression surface. At zero angle of attack (AoA) as the example studied in this paper, a flat pressure surface achieves this purpose. The CFD simulation shows that it obtains low ground sonic boom overpressure of 0.3psf with L/D p = 5.3. Furthermore, the ground pressure signature is not the N shape wave with two strong shock wave pulses, but is in a smooth sin wave shape. The results show that it is possible to remove or achieve very low sonic boom using a supersonic bi-directional flying wing or blended wing body configuration. Future work will optimize the SBiDir-FW concept to achieve high aerodynamic efficiency and maintain low sonic boom.

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Section: Validation Of Sonic Boom Simulationmentioning

confidence: 99%

Toward Zero Sonic-Boom and High Efficiency Supersonic Flight, Part I: A Novel Concept of Supersonic Bi-Directional Flying Wing

Zha

Espinal

2010

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

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“…A set of 4th order and 6th order central differencing schemes are devised to match the same stencil width of the WENO schemes for the viscous terms [19,20]. For turbulent simulations, FASIP has implemented Detached Eddy Simulation (DES) [21,22,23,24,25,26,27], Large Eddy Simulation(LES) [20,28], and Reynolds averaged Navier-Stokes (RANS) [29,19,30,31,32,33,34,35]. An implicit 2nd order time accurate scheme with pseudo time and unfactored Gauss-Seidel line relaxation is employed for time marching.…”

Section: Methodsmentioning

confidence: 99%

Near field Sonic Boom calculation of Benchmark Cases

Gan

Zha²

2015

53rd AIAA Aerospace Sciences Meeting

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This paper validates the accuracy of a high order accuracy CFD code on predicting near field signatures of sonic boom propagation. The flow near the body is solved using a structured grid Euler solver with low diffusion E-CUSP schemes, 3rd order MUSCL scheme, and 3rd and 5th order WENO schemes. Three benchmark cases, including two non-lifting models and one lifting model, are calculated. The predicted results are in good agreement with that of experiment data. For the Delta wing configuration, the mesh provided by the workshop generates a smooth expansion wave at the off-track plane. When the mesh is refined, a shock coalesced by the compression waves from the wing tip is captured and it generates a weak shock wave interacting with the expansion.

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“…The unfactored implicit Gauss-Seidel line relaxation method developed in [30][31][32] by the authors' research group is adopted in this paper. This is the first time that this implicit method is used with a WENO scheme.…”

Section: E Time-marching Methodsmentioning

confidence: 99%

Improvement of Stability and Accuracy for Weighted Essentially Nonoscillatory Scheme

2009

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This paper studies the weights stability and accuracy of the implicit fifth-order weighted essentially nonoscillatory finite difference scheme. It is observed that the weights of the Jiang-Shu weighted essentially nonoscillatory scheme oscillate even for smooth flows. An increased " value of 10 2 is suggested for the weighted essentially nonoscillatory smoothness factors, which removes the weights oscillation and significantly improves the accuracy of the weights and solution convergence. With the improved " value, the weights achieve the optimum value with minimum numerical dissipation in smooth regions and maintain the sensitivity to capture nonoscillatory shock profiles for the transonic flows. The theoretical justification of this treatment is given in the paper. The wall surface boundary condition uses a half-point mesh so that the conservative differencing can be enforced. A third-order accurate finite difference scheme is given to treat wall boundary conditions. The implicit time-marching method with unfactored Gauss-Seidel line relaxation is used with the high-order schemes to achieve a high convergence rate. Several transonic cases are calculated to demonstrate the robustness, efficiency, and accuracy of the methodology. Nomenclature C k = optimal weight IS k = smoothness estimator J = Jacobian of transformation M = Mach number Pr = Prandtl number Pr t = turbulent Prandtl number p = pressure/power used for weighted essentially nonoscillatory scheme q k = heat flux in Cartesian coordinates/third-order polynomial interpolation Re = Reynolds number t = time u, v, w = velocity components in x, y, and z direction x, y, z = Cartesian coordinates = ratio of specific heats U = difference of the conservative variables " = parameter introduced in weighted essentially nonoscillatory scheme = molecular viscosity t = turbulent viscosity , , = generalized coordinates = density ! k = weight Subscripts i, j, k = indices w = wall 1 = freestream Superscripts L, R = left and right sides of the interface n = time level = dimensionless variable

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Calculations of 3D compressible flows using an efficient low diffusion upwind scheme

Cited by 17 publications

References 17 publications

Toward Zero Sonic-Boom and High Efficiency Supersonic Flight, Part I: A Novel Concept of Supersonic Bi-Directional Flying Wing

Toward Zero Sonic-Boom and High Efficiency Supersonic Flight, Part I: A Novel Concept of Supersonic Bi-Directional Flying Wing

Near field Sonic Boom calculation of Benchmark Cases

Improvement of Stability and Accuracy for Weighted Essentially Nonoscillatory Scheme

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