High-order methods for turbulent flows on three-dimensional strand grids. (English) Zbl 1381.76134
Summary: In this paper, we formulate a high-order flux correction method for three-dimensional laminar and turbulent flows on strand grids. Building on previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. Where turbulence modeling is required, a robust version of the Spalart-Allmaras model is employed that accommodates negative values of the turbulence working variable. Fundamental verification and validation studies are considered, which demonstrate the flux correction method achieves high-order accuracy for both laminar and turbulent flows. The high-order flux correction requires only 30 % more walltime to converge when compared to a second-order scheme.
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
References:
| [1] | Allmaras, S., Johnson, F., Spalart, P.: Modifications and clarifications for the implementation of the Spalart-Allmaras turbulence model. Technical Report ICCFD7-1902, 7th International Conference on Computational Fluid Dynamics (2012) · Zbl 1439.76111 |
| [2] | Barth, T.J., Frederickson, P.: Higher order solution of the euler equations on unstructured grids using quadratic reconstruction. AIAA paper 1990-0013, AIAA 28th Aerospace Sciences Meeting, Reno, NV (1990) · Zbl 1408.76345 |
| [3] | Bassi, F., Rebay, S.: High-order accurate discontinuous finite element solution of the 2d euler equations. J. Comput. Phys. 138, 251-285 (1997) · Zbl 0902.76056 · doi:10.1006/jcph.1997.5454 |
| [4] | Benek, J.A., Steger, J.L., Dougherty, F.C.: A flexible grid embedding technique with application to the euler equations. AIAA paper 1983-1944, AIAA 6th Computational Fluid Dynamics Conference, Danvers, MA (1983) · Zbl 1008.65062 |
| [5] | Carpenter, M., Gottlieb, D., Abarbanel, S.: Time-stagle boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes. ICASE Report 93-9, ICASE, Hampton, VA (1993) · Zbl 0832.65098 |
| [6] | Carpenter, M.H., Gottlieb, D., Abarbanel, S.: The stability of numerical boundary treatments for compact high-order finite-difference schemes. J. Comput. Phys. 108(2), 272-295 (1993). doi:10.1006/jcph.1993.1182 · Zbl 0791.76052 · doi:10.1006/jcph.1993.1182 |
| [7] | Delanaye, M., Liu, Y.: Quadratic reconstruction finite volume schemes on 3D arbitrary unstructured polyhedral grids. AIAA paper 1995-3259, AIAA 14th CFD Conference, Norfolk (1999) · Zbl 1305.76058 |
| [8] | Diener, P., Dorband, E., Schnetter, E., Tiglio, M.: Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions. J. Sci. Comput. 32, 109-145 (2007) · Zbl 1120.65092 · doi:10.1007/s10915-006-9123-7 |
| [9] | Fernandez, D.C.D.R., Zingg, D.: High-order compact-stencil summation-by-parts operators for the second derivative with variable coefficients. Technical Report ICCFD7-2803, 7th International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, HI (2012) · Zbl 1072.65118 |
| [10] | Hsieh, T.: An investigation of separated flow about a hemisphere-cylinder at 0- to 19- deg incidence in the mach number range from 0.6 to 1.5. AEDC-TR 76-112, Arnold Engineering Development Center (1976) |
| [11] | Katz, A., Sankaran, V.: An efficient correction method to obtain a formally third-order accurate flow solver for node-centered unstructured grids. J. Sci. Comput. 51, 375-393 (2012) · Zbl 1439.76111 · doi:10.1007/s10915-011-9515-1 |
| [12] | Katz, A., Wissink, A., Sankaran, V., Meakin, R., Sitaraman, J.: Application of strand meshes to complex aerodynamic flow fields. J. Comput. Phys. 230, 6512-6530 (2011) · Zbl 1408.76345 · doi:10.1016/j.jcp.2011.04.036 |
| [13] | Katz, A., Work, D.: High-order flux correction/finite difference schemes for strand grids. J. Comput. Phys. 282, 360-380 (2015) · Zbl 1352.65241 · doi:10.1016/j.jcp.2014.11.019 |
| [14] | Kreiss, H.; Scherer, G.; Boor, CD (ed.), Finite element and finite difference methods for hyperbolic partial differential equations (1974), Massachusetts · Zbl 0355.65085 |
| [15] | Lee, Y.L., Baeder, J.: Implicit hole cutting: a new approach to overset grid connectivity. AIAA paper 2003-4128, AIAA 16th Computational Fluid Dynamics Conference, Orlando, FL (2003) · Zbl 1252.65055 |
| [16] | Magnaudet, J., Riviero, M., Fabre, J.: Accelerated flows past a sphere or spherical bubble. part 1: steady streaming flow. J. Fluid Mech. 284, 97-135 (1995) · Zbl 0848.76063 · doi:10.1017/S0022112095000280 |
| [17] | Mattsson, K.: Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients. J. Sci. Comput. 51, 650-682 (2012) · Zbl 1252.65055 · doi:10.1007/s10915-011-9525-z |
| [18] | Meakin, R., Wissink, A., Chan, W., Pandya, S., Sitaraman, J.: On strand grids for complex flows. AIAA paper 2007-3834, AIAA 18th Computational Fluid Dynamics Conference, Miami, FL (2007) |
| [19] | Nordström, J., Forsberg, K., Adamsson, C., Eliasson, P.: Finite volume methods, unstructured meshes and strict stability for hyperbolic problems. Appl. Numer. Math. 45, 453-473 (2003) · Zbl 1019.65066 · doi:10.1016/S0168-9274(02)00239-8 |
| [20] | Ollivier-Gooch, C., Nejat, A., Michalak, K.: On obtaining high-order finite-volume solutions to the Euler equations on unstructured meshes. AIAA paper 2007-4464, AIAA 18th Computational Fluid Dynamics Conference, Miami, FL (2007) · Zbl 0792.65011 |
| [21] | Pincock, B., Katz, A.: High-order flux correction for viscous flows on arbitrary unstructured grids. AIAA paper, AIAA 21st Computational Fluid Dynamics Conference, San Diego, CA (2013) · Zbl 1299.76161 |
| [22] | Pruppacher, H., Clair, B.L., Hamielec, A.: Some relations between drag and flow pattern of viscous flow past a sphere and cylinder at low and intermediate Reynolds numbers. J. Fluid Mech. 44, 781-791 (1970) · doi:10.1017/S0022112070002148 |
| [23] | Roache, P.: Code verification by the method of manufactured solutions. Trans. ASME 124, 4-10 (2002) |
| [24] | Roy, C.: Review of code and solution verification procedures for computational simulation. J. Comput. Phys. 205, 131-156 (2005) · Zbl 1072.65118 · doi:10.1016/j.jcp.2004.10.036 |
| [25] | Rumsey, C.: NASA Langley turbulence modeling resource. http://turbmodels.larc.nasa.gov (2015) |
| [26] | Sakamoto, H., Haniu, H.: A study on vortex shedding from spheres in a uniform flow. J. Fluids Eng. 112, 386-392 (1990) · doi:10.1115/1.2909415 |
| [27] | Sitaraman, J., Floros, M., Wissink, A., Potsdam, M.: Parallel domain connectivity algorithm for unsteady flow computations using overlapping and adaptive grids. J. Comput. Phys. 229, 4703-4723 (2008) · Zbl 1305.76058 · doi:10.1016/j.jcp.2010.03.008 |
| [28] | Solin, P., Segeth, K., Dolezel, I.: Higher-order finite element methods. CRC Press, Boca Raton (2003) |
| [29] | Spalart, P., Allmaras, S.: A one-equation turbulence model for aerodynamic flows. Recherche Aerospatiale 1, 5-21 (1994) |
| [30] | Steger, J., Dougherty, F., Benek, J.: A chimera grid scheme. Technical Report, ASME Mini-Symposium on Advances in Grid Generation, Houston, TX (1983) |
| [31] | Strand, B.: Summation by parts for finite difference approximation for d/dx. J. Comput. Phys. 110, 47-67 (1994) · Zbl 0792.65011 · doi:10.1006/jcph.1994.1005 |
| [32] | Svärd, M., Carpenter, M., Nordström, J.: A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions. J. Comput. Phys. 225, 1020-1038 (2007) · Zbl 1118.76047 · doi:10.1016/j.jcp.2007.01.023 |
| [33] | Svärd, M., Nordström, J.: A stable high-order finite difference scheme for the compressible Navier-Stokes equations, no-slip wall boundary conditions. J. Comput. Phys. 227, 4805-4824 (2008) · Zbl 1260.76021 · doi:10.1016/j.jcp.2007.12.028 |
| [34] | Taneda, S.: Experimental investigation of wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Jpn. 11, 1104-1108 (1956) · doi:10.1143/JPSJ.11.1104 |
| [35] | Taneda, S.: Visual observations of flow past a sphere at Reynolds numbers between \[10^4104\] and \[10^6106\]. J. Fluid Mech. 85, 187-192 (1978) · doi:10.1017/S0022112078000580 |
| [36] | Tomboulides, A., Orszag, S., Karniadakis, G.: Direct and large eddy simulations of axisymmetric wakes. AIAA paper 93-0546 (1993) |
| [37] | Tong, O., Work, D., Katz, A.: High-order methods for turbulence using strand grids. Technical Report. ICCFD8-0215, 8th International Conference on Computational Fluid Dynamics (ICCFD8), Chengdu, China (2014) |
| [38] | Visbal, M., Gaitonde, D.: On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155-185 (2002) · Zbl 1008.65062 · doi:10.1006/jcph.2002.7117 |
| [39] | Wissink, A.: Helios solver developments including strand meshes. Oral presentation, 11th Symposium on Overset Composite Grids and Solution Technology (2012) |
| [40] | Wissink, A., Katz, A., Chan, W., Meakin, R.: Validation of the strand grid approach. AIAA paper 2009-3792, AIAA 19th Computational Fluid Dynamics Conference, San Antonio, TX (2009) |
| [41] | Wissink, A., Potsdam, M., Sankaran, V., Sitaraman, J., Yang, Z., Mavriplis, D.: A coupled unstructured-adaptive cartesian cfd approach for hover prediction. Technical Report, American Helicopter Society 66th Annual Forum, Phoenix, AZ (2010) |
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