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Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation. (English) Zbl 1299.76099
Summary: A method for generating inflow conditions for direct numerical simulations (DNS) of spatially-developing flows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system. The approach’s robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder. The performance of the technique is also illustrated in a real world application by using noisy large scale PIV measurements. This method denoises experimental velocity fields and reconstructs a continuous trajectory of motion fields from discrete and unstable measurements.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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[1] Druault, P.; Lardeau, S.; Bonnet, J. P.; Coiffet, F.; Delville, J.; Lamballais, E.; Largeau, J. F.; Perret, L., Generation of three-dimensional turbulent inlet conditions for large-eddy simulation, AIAA J., 42, 447, (2004)
[2] Griewank, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Frontiers in Applied Mathematics, (2000), SIAM · Zbl 0958.65028
[3] L. Hascoet, R. Greborio, V. Pascual, Computing adjoints by automatic differentiation with tapenade, Research report, INRIA, 2003.
[4] Keating, A.; Piomelli, U.; Balaras, E.; Kaltenbach, H. J., A priori and a posteriori tests of inflow conditions for large eddy simulation, Phys. Fluids, 16, 4696, (2004) · Zbl 1187.76263
[5] Laizet, S.; Li, N., Incompact3d: a powerful tool to tackle turbulence problems with up to \(O(10^5)\) computational cores, Int. J. Numer. Methods Fluids, 67, 11, 1735-1757, (2011) · Zbl 1419.76481
[6] Laizet, S.; Lamballais, E., High-order compact schemes for incompressible flows: a simple and efficient method with the quasi-spectral accuracy, J. Comput. Phys., 228, 16, 5989-6015, (2009) · Zbl 1185.76823
[7] Le-Dimet, F. X.; Talagrand, O., Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus, 38, A, 97-110, (1986)
[8] Lions, J. L., Optimal control of systems governed by pdes, (1971), Springer-Verlag New York · Zbl 0203.09001
[9] Liu, D.; Nocedal, J., On the limited memory BFGS method for large scale optimization, Math. Program., Ser. B, 45, 3, 503-528, (1989) · Zbl 0696.90048
[10] Lund, T. S.; Wu, X.; Squires, K. D., Generation of inflow data for spatially-developing boundary layer simulations, J. Comput. Phys., 140, 233, (1998) · Zbl 0936.76026
[11] Papadakis, N.; Memin, E., Variational assimilation of fluid motion from image sequences, SIAM J. Imaging Sci., 1, 4, 343-363, (2008) · Zbl 1193.49037
[12] Perret, L.; Delville, J.; Manceau, R.; Bonnet, J. P., Turbulent inflow conditions for large-eddy simulation based on low-order empirical model, Phys. Fluids, 20, 075107, (2008) · Zbl 1182.76598
[13] Zdravkovich, M., Flow around circular cylinder - volume 1: fundamentals, (1997), Oxford University Press Inc New York, United States · Zbl 0882.76004
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