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A comparative study of boundary conditions for the density-based solvers in the framework of OpenFoam. (English) Zbl 1410.76219
Summary: In the framework of OpenFOAM, two methods for the boundary condition treatments are discussed and compared for the density-based solvers, including the strong- and the weak-imposition approach. For the weak-imposition approach, the Riemann method is implemented. For the treatment of subsonic inlet and outlet in the Riemann method, the nonreflective boundary condition based on the finite wave model is adopted and extended to the unstructured grid. With the Riemann method, the boundary condition treatments are transformed into the acquisition of the numerical flux with approximate Riemann solvers at the boundary face, same as that of interior faces. And the information of propagating waves at the boundary is correctly reflected through the usage of approximate Riemann solvers. What is more attractive is that the formal accuracy near the boundary as well as the global accuracy can be preserved without destroying the numerical stability of the simulation. For the strong-imposition approach, the ghost cell method is implemented. In spite of its simplicity, the robustness is not good enough on the unstructured triangular grid. Besides, it has been found that the formal accuracy near the boundary is only first order, thus influencing the solution quality and the global accuracy of the flowfields. Some typical inviscid examples are presented to evaluate the performance of these two methods.
##### MSC:
 76M12 Finite volume methods applied to problems in fluid mechanics 76-04 Software, source code, etc. for problems pertaining to fluid mechanics
##### Software:
FUN3D; OpenFOAM; TAU
Full Text:
##### References:
 [1] Mavriplis, D. J., Unstructured grid techniques, Annu Rev Fluid Mech, 29, 473-514, (1997) [2] Venkatakrishnan, V., A perspective on unstructured grid flow solvers, Tech. Rep., (1995), ICASE Report No. 95-3 [3] Murayam, M.; Nakahashi, K.; Matsushima, K., Unstructured dynamic mesh for large movement and deformation, AIAA-2002-0122, (2002) [4] Schwamborn, D.; Gerhold, T.; Heinrich, R., The DLR TAU-code: recent applications in research and industry, European conference on computational fluid dynamics, TU Delft, The Netherlands, (2006) [5] Biedron, R. T.; Carlson, J.-R.; Derlaga, J. M.; Gnoffo, P. A.; Hammond, D. P.; Jones, W. T.; Kleb, B.; Lee-Rausch, E. M.; Nielsen, E. J.; Park, M. A.; Rumsey, C. L.; Thomas, J. L.; Wood, W. A., FUN3D manual: 13.2, Tech. Rep., (2017) [6] Smith, T. M.; Barone, M. F.; Bond, R. B.; Lorber, A. A.; Baur, D. G., Comparison of reconstruction techniques for unstructured mesh vertex centered finite volume schemes, AIAA-2007-3958, (2007) [7] Caraeni, D.; Hill, D. C., Unstructured-grid third-order finite volume discretization using a multistep quadratic data-reconstruction method, AIAA J, 48, 808-817, (2010) [8] Shima, E.; Kitamura, K.; Haga, T., Green-Gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids, AIAA J, 51, 2740-2747, (2013) [9] Sozer, E.; Brehm, C.; Kiris, C. C., Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered CFD solvers, AIAA-2014-1440, (2014) [10] Thompson, K. W., Time-dependent boundary conditions for hyperbolic systems, J Comput Phys, 68, 1-24, (1987) · Zbl 0619.76089 [11] Thompson, K. W., Time-dependent boundary conditions for hyperbolic systems, II, J Comput Phys, 89, 439-461, (1990) · Zbl 0701.76070 [12] Poinsot, T. J.; Lele, S. K., Boundary conditions for direct simulations of compressible viscous flows, J Comput Phys, 101, 104-129, (1992) · Zbl 0766.76084 [13] Kim, J. W.; Lee, D. J., Generalized characteristic boundary conditions for computational aeroacoustics, AIAA J, 38, 2040-2049, (2000) [14] Kim, J. W.; Lee, D. J., Generalized characteristic boundary conditions for computational aeroacoustics, part 2, AIAA J, 42, 47-55, (2004) [15] Yoo, C. S.; Wang, Y.; Trouvé, A.; Im, H. G., Characteristic boundary conditions for direct simulations of turbulent counterflow flames, Combust Theor Modell, 9, 617-646, (2005) · Zbl 1086.80006 [16] Yoo, C. S.; Im, H. G., Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reaction effects, Combust Theor Modell, 11, 259-586, (2007) · Zbl 1121.80342 [17] Lodato, G.; Domingo, P.; Vervisch, L., Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows, J Comput Phys, 227, 5105-5143, (2008) · Zbl 1388.76098 [18] Gross, A.; Fasel, H. F., Characteristic ghost-cell boundary condition, AIAA J, 45, 302-306, (2007) [19] Motheau, E.; Almgren, A.; Bell, J. B., Navier-Stokes characteristic boundary conditions using ghost cells, AIAA-2017-3625, (2017) [20] Granet, V.; Vermorel, O.; LȨonard, T.; Gicquel, L., Comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids, AIAA J, 48, 2348-2364, (2010) [21] Carlson, J.-R., Inflow/outflow boundary conditions with application to FUN3D, Tech. Rep, (2011), NASA/TM-2011-217181 [22] 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 [23] Bassi, F.; Rebay, S., A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J Comput Phys, 131, 267-279, (1997) · Zbl 0871.76040 [24] Krivodonova, L.; Berger, M., High-order accurate implementation of solid wall boundary conditions in curved geometries, J Comput Phys, 211, 492-512, (2006) · Zbl 1138.76403 [25] Toulorge, T.; Desmet, W., Curved boundary treatments for the discontinuous Galerkin method applied to aeroacoustic propagation, AIAA 2009-3176, (2009) [26] Gao, H.; Wang, Z. J.; Liu, Y., A study of curved boundary representations for 2D high order Euler solvers, J Sci Comput, 44, 323-336, (2010) · Zbl 1203.65032 [27] Zhang, X., A curved boundary treatment for discontinuous Galerkin schemes solving time dependent problems, J Comput Phys, 308, 153-170, (2016) · Zbl 1352.65380 [28] Atkins, H.; Casper, J., Nonreflective boundary conditions for high-order methods, AIAA J, 32, 512-518, (1994) · Zbl 0798.76074 [29] 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) [30] Blazek, J., Computational fluid dynamics: principles and applications, (2001), Elsevier · Zbl 0995.76001 [31] Moukalled, F.; Mangani, L.; Darwish, M., The finite volume method in computational fluid dynamics: an advanced introduction with openfoamë and matlabë, (2016), Springer · Zbl 1329.76001 [32] Toro, E. F., Riemann solvers and numerical methods for fluid dynamics, (2009), Springer · Zbl 1227.76006 [33] Barth, T. J.; Jespersen, D. C., The design and application of upwind schemes on unstructured meshes, AIAA-89-0366, (1989) [34] Venkatakrishnan, V., Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J Comput Phys, 118, 120-130, (1995) · Zbl 0858.76058 [35] Park, J. S.; Yoon, S.-H.; Kim, C., Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids, J Comput Phys, 229, 788-812, (2010) · Zbl 1185.65150 [36] Wang, Z. J.; Fidkowski, K.; Abgrall, R.; Bassi, F.; Caraeni, D.; Cary, A.; Deconinck, H.; Hartmann, R.; Hillewaert, K.; Huynh, H. T.; Kroll, N.; May, G.; Persson, P.-O.; van Leer, B.; Visbal, M., High-order CFD methods: current status and perspective, Int J Numer Meth Fluids, 72, 811-845, (2013) [37] Dong, Y.; Deng, X.; Xu, D.; Wang, G., Reevaluation of high-order finite difference and finite volume algorithms with freestream preservation satisfied, Comput Fluids, 158, 343-352, (2017) · Zbl 1390.76424
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