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A low-dissipative solver for turbulent compressible flows on unstructured meshes, with openfoam implementation. (English) Zbl 1390.76492

Summary: We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of the convective terms in the Navier-Stokes equations relies on a robust energy-preserving numerical flux, and numerical diffusion inherited from the AUSM scheme is added limited to the vicinity of shock waves, or wherever spurious numerical oscillations are sensed. The solver is capable of conserving the total kinetic energy in the inviscid limit, and it bears sensibly less numerical diffusion than typical industrial solvers, with incurred greater predictive power, as demonstrated through a series of test cases including DNS, LES and URANS of turbulent flows. Simplicity of implementation in existing popular solvers such as OpenFOAM is also highlighted.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76F50 Compressibility effects in turbulence
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[1] Orszag, S.; Patterson, G., Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys Rev Lett, 28, 2, 76, (1972)
[2] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J Fluid Mech, 177, 133-166, (1987) · Zbl 0616.76071
[3] Schlatter, P.; Örlü, R., Assessment of direct numerical simulation data of turbulent boundary layers, J Fluid Mech, 659, 116-126, (2010) · Zbl 1205.76139
[4] Sillero, J.; Jiménez, J.; Moser, R., One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to \(\delta^+ \approx\) 2000, Phys Fluids (1994-present), 25, 10, 105102, (2013)
[5] Bernardini, M.; Pirozzoli, S.; Orlandi, P., Velocity statistics in turbulent channel flow up to R\(e_\tau = 4000\), J Fluid Mech, 742, 171-191, (2014)
[6] Kim, S.; Choudhury, D.; Patel, B., Computations of complex turbulent flows using the commercial code FLUENT, Modeling complex turbulent flows, 259-276, (1999), Springer
[7] Iaccarino, G., Predictions of a turbulent separated flow using commercial CFD codes, J Fluids Eng, 123, 4, 819-828, (2001)
[8] Mahesh, K.; Constantinescu, G.; Apte, S.; Iaccarino, G.; Ham, F.; Moin, P., Large-eddy simulation of reacting turbulent flows in complex geometries, J Appl Mech, 73, 3, 374-381, (2006) · Zbl 1111.74539
[9] Bernardini, M.; Modesti, D.; Pirozzoli, S., On the suitability of the immersed boundary method for the simulation of high-Reynolds-number separated turbulent flows, Comput Fluids, 130, 84-93, (2016) · Zbl 1390.76132
[10] Hussaini, M.; Zang, T., Spectral methods in fluid dynamics, Annu Rev Fluid Mech, 19, 1, 339-367, (1987) · Zbl 0636.76009
[11] Lele, S., Compact finite difference schemes with spectral-like resolution, J Comput Phys, 103, 1, 16-42, (1992) · Zbl 0759.65006
[12] Harlow, F.; Welch, J., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys Fluids, 8, 12, 2182, (1965) · Zbl 1180.76043
[13] Orlandi, P., Fluid flow phenomena: a numerical toolkit, 55, (2012), Springer Science & Business Media
[14] Jameson, A.; Schmidt, W.; Turkel, E., Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA Pap, 12-59, 1981, (1981)
[15] Suresh, A.; Huynh, H., Accurate monotonicity-preserving schemes with Runge-Kutta time stepping, J Comput Phys, 136, 1, 83-99, (1997) · Zbl 0886.65099
[16] Pirozzoli, S., Conservative hybrid compact-WENO schemes for shock-turbulence interaction, J Comput Phys, 178, 1, 81-117, (2002) · Zbl 1045.76029
[17] Pirozzoli, S., Numerical methods for high-speed flows, Annu Rev Fluid Mech, 43, 163-194, (2011) · Zbl 1299.76103
[18] Hickel, S.; Egerer, C.; Larsson, J., Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction, Phys Fluids (1994-present), 26, 10, 106101, (2014)
[19] Patankar, S.; Spalding, D., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int J Heat Mass Transf, 15, 10, 1787-1806, (1972) · Zbl 0246.76080
[20] Ferziger, J.; Peric, M., Computational methods for fluid dynamics, (2012), Springer Science & Business Media · Zbl 0869.76003
[21] Mittal, R.; Moin, P., Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows, AIAA J, 35, 8, 1415-1417, (1997) · Zbl 0900.76336
[22] Nicolaides, R.; Wu, X., Covolume solutions of three-dimensional div-curl equations, SIAM J Numer Anal, 34, 6, 2195-2203, (1997) · Zbl 0889.35006
[23] Ducros, F.; Laporte, F.; Souleres, T.; Guinot, V.; Moinat, P.; Caruelle, B., High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows, J Comput Phys, 161, 1, 114-139, (2000) · Zbl 0972.76066
[24] Perot, B., Conservation properties of unstructured staggered mesh schemes, J Comput Phys, 159, 1, 58-89, (2000) · Zbl 0972.76068
[25] Ham, F.; Lien, F.; Strong, A., A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids, J Comput Phys, 177, 1, 117-133, (2002) · Zbl 1066.76044
[26] Subbareddy, P.; Candler, G., A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows, J Comput Phys, 228, 5, 1347-1364, (2009) · Zbl 1157.76029
[27] Shoeybi, M.; Svärd, M.; Ham, F.; Moin, P., An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids, J Comput Phys, 229, 17, 5944-5965, (2010) · Zbl 1425.76108
[28] Mendez, S.; Shoeybi, M.; Sharma, A.; Ham, F.; Lele, S.; Moin, P., Large-eddy simulations of perfectly expanded supersonic jets using an unstructured solver, AIAA J, 50, 5, 1103-1118, (2012)
[29] Weller, H.; Hrvoje, G. T.; Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput Phys, 12, 6, 620-631, (1998)
[30] Kurganov, A.; Tadmor, E., New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J Comput Phys, 160, 1, 241-282, (2000) · Zbl 0987.65085
[31] Vuorinen, V.; Larmi, M.; Schlatter, P.; Fuchs, L.; Boersma, B., A low-dissipative, scale-selective discretization scheme for the Navier-Stokes equations, Comput Fluids, 70, 195-205, (2012) · Zbl 1365.76202
[32] Vuorinen, V.; Keskinen, J.; Duwig, C.; Boersma, B., On the implementation of low-dissipative Runge-Kutta projection methods for time dependent flows using openfoam^{®;}, Comput Fluids, 93, 153-163, (2014) · Zbl 1391.76006
[33] Shen, C.; Sun, F.; Xia, X., Implementation of density-based solver for all speeds in the framework of openfoam, Comput Phys Commun, 185, 10, 2730-2741, (2014) · Zbl 1360.76010
[34] Shen, C.; Xia, X.-L.; Wang, Y.-Z.; Yu, F.; Jiao, Z.-W., Implementation of density-based implicit Lu-sgs solver in the framework of openfoam, Adv Eng Softw, 91, 80-88, (2016)
[35] Liou, M.; Steffen, C., A new flux splitting scheme, J Comput Phys, 107, 1, 23-39, (1993) · Zbl 0779.76056
[36] Cerminara, M.; Ongaro, T. E.; Berselli, L., ASHEE-1.0: a compressible, equilibrium-Eulerian model for volcanic ash plumes, Geosci Model Dev, 9, 2, 697-730, (2016)
[37] Pirozzoli, S., Generalized conservative approximations of split convective derivative operators, J Comput Phys, 229, 19, 7180-7190, (2010) · Zbl 1426.76485
[38] Pirozzoli, S., Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates, J Comput Phys, 230, 2997-3014, (2011) · Zbl 1316.76064
[39] Ducros, F.; Ferrand, V.; Nicoud, F.; Weber, C.; Darracq, D.; Gacherieu, D., Large-eddy simulation of the shock/turbulence interaction, J Comput Phys, 152, 2, 517-549, (1999) · Zbl 0955.76045
[40] Hirsch, C., Numerical computation of internal and external flows: the fundamentals of computational fluid dynamics, (2007), Butterworth-Heinemann
[41] Blaisdell, G.; Mansour, N.; Reynolds, W., Numerical simulation of compressible homogeneous turbulence, Report, TF-50, (1991), Thermosciences Division,Dep. Mech. Eng., Stanford University
[42] Duponcheel, M.; Orlandi, P.; Winckelmans, G., Time-reversibility of the Euler equations as a benchmark for energy conserving schemes, J Comput Phys, 227, 19, 8736-8752, (2008) · Zbl 1259.76036
[43] Modesti, D.; Pirozzoli, S., Reynolds and Mach number effects in compressible turbulent channel flow, Int J Heat Fluid Flow, 59, 33-49, (2016)
[44] Coleman, G.; Kim, J.; Moser, R., A numerical study of turbulent supersonic isothermal-wall channel flow, J Fluid Mech, 305, 159-183, (1995) · Zbl 0960.76517
[45] Lechner, R.; Sesterhenn, J.; Friedrich, R., Turbulent supersonic channel flow, J Turbul, 2, 1, 1-25, (2001) · Zbl 1001.76510
[46] Bernardini, M.; Pirozzoli, S.; Quadrio, M.; Orlandi, M., Turbulent channel flow simulations in convecting reference frames, J Comput Phys, 232, 1, 1-6, (2013)
[47] Catalano, P.; Wang, M.; Iaccarino, G.; Moin, P., Numerical simulation of the flow around a circular cylinder at high Reynolds numbers, Int J Heat Fluid Flow, 24, 4, 463-469, (2003)
[48] Shih, W.; Wang, C.; Coles, D.; Roshko, A., Experiments on flow past rough circular cylinders at large Reynolds numbers, J Wind Eng Indust Aerodyn, 49, 1, 351-368, (1993)
[49] Warschauer, K.; Leene, J., Experiments on mean and fluctuating pressures of circular cylinders at cross flow at very high Reynolds numbers, Proceedingsinternationalconference on wind effects on buildings and structures, 305-315, (1971)
[50] Zdravkovich, M., Flow around circular cylinders, Fundamentals, Vol. 1, (1997) · Zbl 0882.76004
[51] Spalart, P.; Allmaras, S., A one equation turbulence model for aerodinamic flows, AIAA J, 94, 6-10, (1992)
[52] Spalart, P.; Jou, W.; Strelets, M.; Allmaras, S., Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach, Adv DNS/LES, 1, 4-8, (1997)
[53] Piomelli, U.; Balaras, E., Wall-layer models for large-eddy-simulations, Annu Rev Fluid Mech, 34, 349-374, (2002) · Zbl 1006.76041
[54] Spalding, D., A single formula for the “law of the wall”, J Appl Mech, 28, 3, 455-458, (1961) · Zbl 0098.17603
[55] Woodward, P.; Colella, P., The numerical simulation of two-dimensional fluid flow with strong shocks, J Comput Phys, 54, 1, 115-173, (1984) · Zbl 0573.76057
[56] Emery, A., An evaluation of several differencing methods for inviscid fluid flow problems, J Comput Phys, 2, 3, 306-331, (1968) · Zbl 0155.21102
[57] Liou, M., A sequel to AUSM, part II: AUSM+-up for all speeds, J Comput Phys, 214, 1, 137-170, (2006) · Zbl 1137.76344
[58] Schmitt, V.; Charpin, F., Pressure distributions on the ONERA-M6-wing at transonic Mach numbers, AGARD Advisory Report, AR-138, (1979)
[59] Cook, P.; Firmin, M.; McDonald, M., Aerofoil RAE 2822: pressure distributions, and boundary layer and wake measurements, AGARD Advisory Report, AR-138, (1979)
[60] Coakley, T., Numerical simulation of viscous transonic airfoil flows, 25th AIAA aerospace sciences meeting, 416, (1987)
[61] Nelson C., Dudek J.. RAE 2822 transonic airfoil: study 5. 2009. https://www.grc.nasa.gov/WWW/wind/valid/raetaf/raetaf05/raetaf05.html; Nelson C., Dudek J.. RAE 2822 transonic airfoil: study 5. 2009. https://www.grc.nasa.gov/WWW/wind/valid/raetaf/raetaf05/raetaf05.html
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