A high-order flux reconstruction method for 3D mixed overset meshes. (English) Zbl 07211840

Summary: The use of overset meshes can significantly simplify grid generation for complex configurations, and is particularly desired for moving boundary problems as remeshing is often unnecessary. In the present study, we develop a high-order flux reconstruction (FR) solver for mixed overset meshes including the near-body, and background meshes. The main objective is to achieve uniformly high order accuracy in the entire computational domain on both the near body and the background grids. Two different approaches to handle the overset interfaces are evaluated for accuracy, efficiency and robustness. Waves passing across the overset interfaces are tested with both smooth and discontinuous waves. In the present study, we focus on non-moving boundary problems, and demonstrate the overall methodology for steady and unsteady flow problems.


76-XX Fluid mechanics
Full Text: DOI


[1] Benek, J.; Steger, J.; Dougherty, F. C., A flexible grid embedding technique with application to the euler equations, 6th computational fluid dynamics conference danvers, 1944 (1983)
[2] Benek, J.; Buning, P.; Steger, J., A 3-D chimera grid embedding technique, 7th computational physics conference, 1523 (1985)
[3] Pärt-Enander, E.; Sjögreen, B., Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems, Comput. fluids, 23, 3, 551-574 (1994) · Zbl 0813.76071
[4] Henshaw, W. D., A fourth-order accurate method for the incompressible navier-stokes equations on overlapping grids, J Comput Phys, 113, 1, 13-25 (1994) · Zbl 0808.76059
[5] Fujii, K., Unified zonal method based on the fortified solution algorithm, J Comput Phys, 118, 1, 92-108 (1995) · Zbl 0830.76069
[6] Wang, Z. J., A conservative interface algorithm for moving chimera (overlapped) grids, Int J Comut Fluid Dyn, 10, 3, 255-265 (1998) · Zbl 0934.76051
[7] Nakahashi, K.; Togashi, F.; Sharov, D., Intergrid-boundary definition method for overset unstructured grid approach, AIAA J, 38, 11, 2077-2084 (2000)
[8] Loehner, R.; Sharov, D.; Luo, H.; Ramamurti, R., Overlapping unstructured grids, 39th aerospace sciences meeting and exhibit, 439 (2001)
[9] Sherer, S.; Scott, J., Development and validation of a high-order overset grid flow solver, 32nd AIAA fluid dynamics conference and exhibit, 2733 (2002)
[10] Kannan, R.; Wang, Z. J., Overset adaptive cartesian/prism grid method for stationary and moving-boundary flow problems, AIAA J, 45, 7, 1774-1779 (2007)
[11] Carrica, P.; Huang, J.; Noack, R.; Kaushik, D.; Smith, B.; Stern, F., Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant, Comput Fluids, 39, 7, 1095-1111 (2010) · Zbl 1242.76198
[12] Lee, B.-S.; Jung, M.-S.; Kwon, O.-J.; Kang, H.-J., Numerical simulation of rotor-fuselage aerodynamic interaction using an unstructured overset mesh technique, Int J Aeronaut Space Sci, 11, 1, 1-9 (2010)
[13] Shenoy, R.; Smith, M. J.; Park, M. A., Unstructured overset mesh adaptation with turbulence modeling for unsteady aerodynamic interactions, J Aircr, 51, 1, 161-174 (2014)
[14] Wang, Z. J., A fully conservative interface algorithm for overlapped grids, J Comput Phys, 122, 1, 96-106 (1995) · Zbl 0835.76081
[15] Wang, Z. J.; Hariharan, N.; Chen, R., Recent development on the conservation property of chimera, Int J Comut Fluid Dyn, 15, 4, 265-278 (2001) · Zbl 1061.76050
[16] Lee, K. R.; Park, J. H.; Kim, K. H., High-order interpolation method for overset grid based on finite volume method, AIAA J, 49, 7, 1387-1398 (2011)
[17] Sherer, S. E.; Scott, J. N., High-order compact finite-difference methods on general overset grids, J Comput Phys, 210, 2, 459-496 (2005) · Zbl 1113.76068
[18] Nakahashi, K.; Togashi, F.; Sharov, D., Intergrid-boundary definition method for overset unstructured grid approach, AIAA J, 38, 11, 2077-2084 (2000)
[19] Boger, D.; Dreyer, J., Prediction of hydrodynamic forces and moments for underwater vehicles using overset grids, 44th AIAA Aerospace Sciences Meeting and Exhibit, 1148 (2006)
[20] Ahmad, J.; Duque, E. P., Helicopter rotor blade computation in unsteady flows using moving overset grids, J Aircr, 33, 1, 54-60 (1996)
[21] Noack, R., SUGGAR: a general capability for moving body overset grid assembly, 17th AIAA computational fluid dynamics conference, 5117 (2005)
[22] Wang, Z. J.; Fidkowski, K.; Abgrall, R.; Bassi, F.; Caraeni, D.; Cary, A., High-order CFD methods: current status and perspective, Int J Numer Methods Fluids, 72, 8, 811-845 (2013)
[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, 2, 267-279 (1997) · Zbl 0871.76040
[24] Cockburn, B.; Karniadakis, G. E.; Shu, C.-W., The development of discontinuous galerkin methods, Discontinuous Galerkin Methods, 3-50 (2000), Springer · Zbl 0989.76045
[25] Cockburn, B.; Shu, C.-W., Foreword, J Sci Comput, 40, 1, 1-3 (2009)
[26] Shu, C.-W., Discontinuous galerkin method for time-dependent problems: survey and recent developments, Recent developments in discontinuous Galerkin finite element methods for partial differential equations, 25-62 (2014), Springer · Zbl 1282.65122
[27] Kopriva, D. A., A staggered-grid multidomain spectral method for the compressible navier-Stokes equations, J Comput Phys, 143, 1, 125-158 (1998) · Zbl 0921.76121
[28] Liu, Y.; Vinokur, M.; Wang, Z. J., Spectral difference method for unstructured grids i: basic formulation, J Comput Phys, 216, 2, 780-801 (2006) · Zbl 1097.65089
[29] Wang, Z. J., High-order spectral volume method for benchmark aeroacoustic problems, 41st Aerospace Sciences Meeting and Exhibit, 880 (2003)
[30] Liu, Y.; Vinokur, M.; Wang, Z. J., Spectral (finite) volume method for conservation laws on unstructured grids v: extension to three-dimensional systems, J Comput Phys, 212, 2, 454-472 (2006) · Zbl 1085.65099
[31] Sun, Y.; Wang, Z. J.; Liu, Y., Spectral (finite) volume method for conservation laws on unstructured grids VI: extension to viscous flow, J Comput Phys, 215, 1, 41-58 (2006) · Zbl 1140.76381
[32] Huynh, H., A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, 18th AIAA Computational Fluid Dynamics Conference, 4079 (2007)
[33] Wang, Z. J.; Gao, H., A unifying lifting collocation penalty formulation including the discontinuous galerkin, spectral volume/difference methods for conservation laws on mixed grids, J Comput Phys, 228, 21, 8161-8186 (2009) · Zbl 1173.65343
[34] Haga, T.; Gao, H.; Wang, Z. J., A high-order unifying discontinuous formulation for the navier-Stokes equations on 3d mixed grids, Math Model Nat Phenom, 6, 3, 28-56 (2011) · Zbl 1239.76044
[35] Wang, Z. J., High-order methods for the euler and navier-Stokes equations on unstructured grids, Prog Aerosp Sci, 43, 1-3, 1-41 (2007)
[36] Huynh, H.; Wang, Z. J.; Vincent, P. E., High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids, Comput Fluids, 98, 209-220 (2014) · Zbl 1390.65123
[37] Wang, Z. J., A perspective on high-order methods in computational fluid dynamics, Science China Phys Mech Astron, 59, 1, 614701 (2016)
[38] Liu, X.-D.; Osher, S.; Chan, T., Weighted essentially non-oscillatory schemes, J Comput Phys, 115, 1, 200-212 (1994) · Zbl 0811.65076
[39] Tsoutsanis, P.; Antoniadis, A. F.; Jenkins, K. W., Improvement of the computational performance of a parallel unstructured WENO finite volume CFD code for implicit large eddy simulation, Comput Fluids, 173, 157-170 (2018) · Zbl 1410.76268
[40] Tsoutsanis, P., Stencil selection algorithms for WENO schemes on unstructured meshes, J. Comput. Phys.X, 4, 100037 (2019)
[41] Ivan, L.; Groth, C. P., High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows, J Comput Phys, 257, 830-862 (2014) · Zbl 1349.76341
[42] Dumbser, M., Arbitrary high order PNPM schemes on unstructured meshes for the compressible navier-Stokes equations, Comput. Fluids, 39, 1, 60-76 (2010) · Zbl 1242.76161
[43] Clain, S.; Diot, S.; Loubère, R., A high-order finite volume method for systems of conservation lawsmulti-dimensional optimal order detection (MOOD), J Comput Phys, 230, 10, 4028-4050 (2011) · Zbl 1218.65091
[44] Galbraith, M.; Orkwis, P.; Benek, J., Extending the discontinuous Galerkin scheme to the chimera overset method, 20th AIAA computational fluid dynamics conference, 3409 (2011)
[45] Galbraith, M. C.; Benek, J. A.; Orkwis, P. D.; Turner, M. G., A discontinuous galerkin scheme for chimera overset viscous meshes on curved geometries, Comput Fluids, 119, 176-196 (2015) · Zbl 1390.76314
[46] Brazell, M. J.; Sitaraman, J.; Mavriplis, D. J., An overset mesh approach for 3D mixed element high-order discretizations, J Comput Phys, 322, 33-51 (2016) · Zbl 1351.76050
[47] Crabill, J.; Witherden, F. D.; Jameson, A., A parallel direct cut algorithm for high-order overset methods with application to a spinning golf ball, J Comput Phys, 374, 692-723 (2018) · Zbl 1416.76103
[48] Crabill, J. A.; Sitaraman, J.; Jameson, A., A high-order overset method on moving and deforming grids, AIAA modeling and simulation technologies conference, 3225 (2016)
[49] Harris, R. E.; Arslanbekov, R. R.; Collins, E.; Luke, E. A., Validation of overset discontinuous Galerkin and hybrid RANS/LES method for jet noise prediction, 46th AIAA fluid dynamics conference, 3334 (2016)
[50] Nastase, C.; Mavriplis, D.; Sitaraman, J., An overset unstructured mesh discontinuous Galerkin approach for aerodynamic problems, 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 195 (2011)
[51] Grinstein, F. F.; Margolin, L. G.; Rider, W. J., Implicit large eddy simulation: computing turbulent fluid dynamics (2007), Cambridge university press · Zbl 1135.76001
[52] Uranga, A.; Persson, P.-O.; Drela, M.; Peraire, J., Implicit large eddy simulation of transition to turbulence at low reynolds numbers using a discontinuous galerkin method, Int J Numer Methods Eng, 87, 1-5, 232-261 (2011) · Zbl 1242.76085
[53] Vermeire, B. C.; Nadarajah, S.; Tucker, P. G., Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme, Int J Numer Methods Fluids, 82, 5, 231-260 (2016)
[54] Godunov, S. K., A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Matematicheskii Sbornik, 89, 3, 271-306 (1959) · Zbl 0171.46204
[55] Roe, P. L., Approximate riemann solvers, parameter vectors, and difference schemes, J Comput Phys, 43, 2, 357-372 (1981) · Zbl 0474.65066
[56] Rusanov, V. V., Calculation of Interaction of Non-Steady Shock Waves with Obstacles (1962), NRC, Division of Mechanical Engineering
[57] Meakin, R., Object X-rays for cutting holes in composite overset structured grids, 15th AIAA computational fluid dynamics conference, 2537 (2001)
[58] Chesshire, G.; Henshaw, W. D., Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90, 1, 1-64 (1990) · Zbl 0709.65090
[59] Lee, Y.; Baeder, J., Implicit hole cutting-a new approach to overset grid connectivity, 16th AIAA Computational Fluid Dynamics Conference, 4128 (2003)
[60] Roget, B.; Sitaraman, J., Robust and efficient overset grid assembly for partitioned unstructured meshes, J. Comput. Phys, .260, 1-24 (2014) · Zbl 1349.65669
[61] TIOGA, (https://github.com/jsitaraman/tioga).
[62] Gottschalk, S.; Lin, M. C.; Manocha, D., OBBTree: A hierarchical structure for rapid interference detection, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, 171-180 (1996), ACM
[63] Galbraith, M. C., A Discontinuous Galerkin Chimera Overset Solver (2013), University of Cincinnati, Ph.D. thesis
[64] Chen, R.; Wang, Z. J., Fast, block lower-upper symmetric gauss-Seidel scheme for arbitrary grids, AIAA J, 38, 12, 2238-2245 (2000)
[65] Jameson, A.; Yoon, S., Lower-upper implicit schemes with multiple grids for the euler equations, AIAA J, 25, 7, 929-935 (1987)
[66] Yee, H. C.; Sandham, N. D.; Djomehri, M. J., Low-dissipative high-order shock-capturing methods using characteristic-based filters, J Comput Phys, 150, 1, 199-238 (1999) · Zbl 0936.76060
[67] Spiegel, S. C.; Huynh, H.; DeBonis, J. R., A survey of the isentropic euler vortex problem using high-order methods, 22nd AIAA Computational Fluid Dynamics Conference, 2444 (2015)
[68] Lu Q., Liu G., Ming P., Wang Z.J. The applications of a low-dissipation limiter in the FR/CPR method. J Aerosp Power(Submitted).
[69] Ims, J.; Duan, Z.; Wang, Z. J., meshCurve: an automated low-order to high-order mesh generator, 22nd AIAA computational fluid dynamics conference, 2293 (2015)
[70] Taneda, S., Experimental investigation of the wake behind a sphere at low reynolds numbers, J Phys Soc Jpn, 11, 10, 1104-1108 (1956)
[71] Sun, Y.; Wang, Z. J.; Liu, Y., High-order multidomain spectral difference method for the navier-Stokes equations on unstructured hexahedral grids, Commun Comput Phys, 2, 2, 310-333 (2007) · Zbl 1164.76360
[72] The 4th International Workshop on High-Order CFD Methods, T106A turbine blade case, (https://how4.cenaero.be/content/as2-spanwise-periodic-dnsles-transitional-turbine-cascades).
[73] Stadtmüller, P., Investigation of wake-induced transition on the LP turbine cascade T106 A-EIZ, DFG-Verbundprojekt Fo, 136, 11 (2001)
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