Implicit multigrid schemes for challenging aerodynamic simulations on block-structured grids

Cagnone, Jean-Sebastien; Sermeus, Kurt; Nadarajah, Siva; Laurendeau, Éric

doi:10.1016/j.compfluid.2011.01.014

Cited by 19 publications

(10 citation statements)

References 46 publications

(55 reference statements)

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“…Two turbulent models are employed here, the Spalart-Allmaras and k-ω-SST. In figure 1, the pressure coefficient over the airfoil is presented and compared with numerical results of Cagnone et al 11 and experimental data of Cook et al 10 . In figure 2, the convergence rate for the L 2 norm of the averaged density residual (figure 2(a)) and the turbulence variables (figure 2(b)) are presented.…”

Section: Nscodementioning

confidence: 94%

“…These specifications represent test case 9 of Cook et al 10 , who provided the experimental data. The test case has been numerically simulated by Cagnone et al 11 using the Bombardier Aerospace flow solver, FANSC 1,2 . For comparison, the same structured C-grids as 11 are employed with 288x64 and 576x128 grid points.…”

Section: Nscodementioning

confidence: 99%

“…The test case has been numerically simulated by Cagnone et al 11 using the Bombardier Aerospace flow solver, FANSC 1,2 . For comparison, the same structured C-grids as 11 are employed with 288x64 and 576x128 grid points. These grids results into an averaged y + of 1 for the coarser and 0.5 for the finer grids.…”

Section: Nscodementioning

confidence: 99%

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A Two-Dimensional/Infinite Swept Wing Navier-Stokes Solver

Ghasemi

Mosahebi

Laurendeau

2014

52nd Aerospace Sciences Meeting

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An efficient infinite swept wing (ISW) model has been developed and implemented within the two-dimensionalReynolds-Averaged Navier-Stokes (RANS) flow solver NSCODE. The method is devised to simulate 3D RANS simulation over an ISW with the computational cost of one 2D flow solution. A by-product is that only a simple 2D grid of the unswept airfoil is needed for any wing sweep angle, making for a fast solution algorithm suitable for aircraft preliminary sizing studies. Using a loosely coupled scheme for the transverse flow equation, the efficiency of the 2D iterative numerical scheme has been maintained. Validation and verification of the results is performed using analytical models, as well as through comparisons with solutions from the 3D RANS solver NSMB and from experiments. The results illustrate the accuracy and capability of the developed method for this class of flow problems. Nomenclature AC = Aircraft ISW = Infinite Swept Wing Sweep angle = Λ AC angle of attack = α x ,y, z = Aircraft axis system (m) x', y', z' = Local wing coordinate system (m) u, v ,w = Flow speed component in AC axis (m/s) u', v', w' = Flow speed component in Local axis (m/s) , = 3D Rotation matrix of angle around the vector C l = Lift coefficient M = Mach number C lα = Lift curve slope Re c = Reynolds number based on chord

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Section: Nscodementioning

confidence: 94%

Section: Nscodementioning

confidence: 99%

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A Two-Dimensional/Infinite Swept Wing Navier-Stokes Solver

Ghasemi

Mosahebi

Laurendeau

2014

52nd Aerospace Sciences Meeting

Self Cite

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“…But in general the results presented were restricted to 2-D and a straightforward implementation of these methods into an unstructured 3-D code was not clear. By Cagnone et al [11] similar methods were introduced into a block-structured code and the superiority of the method when compared with explicit or point-Jacobi preconditioned Runge-Kutta methods (see van Leer and Langer [12,13]) was shown also for 3-D flows. However, even by Cagnone et al [11] convergence of the turbulent flow equation given by an SA model was not shown.…”

mentioning

confidence: 99%

“…Different kinds of smoothers are derived from a general implicit Runge-Kutta method. It was shown by Langer [14] that, from such a general point of view, it is possible to derive many well-known solution techniques in the computational fluid dynamics (CFD) literature, such as the ones previously mentioned [6][7][8]11], line implicit methods [15][16][17][18][19], point implicit [5,12,13], and even explicit Runge-Kutta methods [2]. All these methods can be interpreted as simplified Newton methods, and they differ with respect to their approximation to the Jacobian and the methods to (approximately) solve the arising linear systems.…”

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confidence: 99%

Investigation and Comparison of Implicit Smoothers Applied in Agglomeration Multigrid

2015

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A straightforward implicit smoothing method implemented in several codes solving the Reynolds-averaged Navier-Stokes equations is the lower-upper symmetric Gauss-Seidel method. It was proposed several years ago and is attractive to implement because of its low memory requirements and low operation count. Since, for many examples, often a severe restriction of the Courant-Friedrichs-Lewy number and loss of robustness are observed, it is the goal of this paper to revisit the lower-upper symmetric Gauss-Seidel implementation and to discuss several alternative implicit smoothing strategies used within an agglomeration multigrid for unstructured meshes. The starting point is a full implicit multistage Runge-Kutta method. Based on this method, several additional features and simplifications are developed and suggested, such that the implicit method is applicable to high-Reynolds-number viscous flows; that is, the required matrices fit into the fast memory of the cluster hardware and the arising linear systems can be approximately solved efficiently. To this end, the focus is on simplifications of the Jacobian, as well as efficient iterative approximate solution methods. To significantly improve the approximate linear solution methods, grid anisotropy is taken care of for approximately solving both the linear systems and the agglomeration strategy. The procedure creating coarse-grid meshes is extended by strategies identifying structured parts of the mesh. This seems to improve the quality of coarse-grid meshes in the way that an overall better reliability of the multigrid can be observed. Furthermore, grid information is exploited within the iterative solution methods for the linear systems. Numerical examples demonstrate the gain with respect to reliability and efficiency.

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Spatial accuracy and performance of a mixed‐order, explicit multi‐stage method for unsteady flows

Waltz

2012

Numerical Methods in Fluids

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SUMMARYWe assess the spatial accuracy and performance of a mixed‐order, explicit multi‐stage method in which an inexpensive low‐order scheme is used for the initial stages, and a more expensive high‐order scheme is used for the final stage only. Compared with the use of a high‐order scheme for all stages, we observe that the mixed‐order scheme achieves comparable accuracy and convergence while providing a speed‐up of a factor of two on mesh sizes of O(106 − 107) tetrahedron. For calculations with significant adaptive mesh refinement, a more modest speed‐up of 30% is obtained. Published 2012. This article is a US Government work and is in the public domain in the USA.

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Implicit multigrid schemes for challenging aerodynamic simulations on block-structured grids

Cited by 19 publications

References 46 publications

A Two-Dimensional/Infinite Swept Wing Navier-Stokes Solver

A Two-Dimensional/Infinite Swept Wing Navier-Stokes Solver

Investigation and Comparison of Implicit Smoothers Applied in Agglomeration Multigrid

Spatial accuracy and performance of a mixed‐order, explicit multi‐stage method for unsteady flows

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