Attenuating and enhancing properties of the approximate deconvolution method based on higher - order explicit and compact filters

Caban, L.; Tyliszczak, A.

doi:10.24423/aom.3996

Artykuł - szczegóły

Tytuł artykułu

Attenuating and enhancing properties of the approximate deconvolution method based on higher - order explicit and compact filters

Autorzy

Caban L. , Tyliszczak A.

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

DOI

10.24423/aom.3996

Warianty tytułu

Języki publikacji

Abstrakty

We analyse the accuracy of a deconvolution (inverse filtering) method in 1D and 2D periodic domains. The deconvolution is performed by applying the iterative van Cittert method using explicit and compact filters of the 2nd to 8th order. We consider cases in which an approximate inverse filter G^-1_α formulated to deconvolve an original function from a filtered one (f = G⁎f) is constructed based on: (a) G the same as used to define f = G⁎f; (b) G different than the one used to define f = G⁎f. In case (a), the convergence rate of the deconvolution process is much better when compact filters are used. This is attributed to a flatter transfer function of this type of filter and thus a smaller deterioration of the input function f. Case (b) reflects a real situation in which the precise definition of a basic filter G used in f = G ⁎ f is unknown. We found that when G^-1_α is formulated based on G of a higher order than the one used to define f the reconstructed function f^⁎ = G^-1_α⁎f is suppressed compared to the original function f. On the other hand, the deconvolution process performed with the use of G^-1_α defined based on G of a lower order than the order of the basic filter significantly amplifies the reconstructed function f^⁎. As a result, the function f^⁎ contains more energy than the function f, especially in the range of small and high-frequency scales. This effect is particularly strong when explicit filters of different orders are used. The impact of the filter type in the practical application of deconvolution is demonstrated based on large eddy simulations (LES) of a 2D decaying homogenous turbulent flow. LES combined with an approximate deconvolution method (ADM) for the computation of sub-filter terms shows better accuracy than in the case when these terms are modelled using the classical Smagorinsky model or when they are neglected (no-model approach). This analysis consists of comparisons of the evolution of total energy, energy spectra, and higher-order moments (variance, skewness, kurtosis) of the velocity components and vorticity. We found that more accurate results are obtained when the deconvolution is performed using the explicit filters even if the deconvolution process based on the compact filters was found to converge faster in 1D and 2D test cases. Most likely this is because in the performed LES the explicit filters correspond better to an unknown filter induced by discretisation.

Słowa kluczowe

explicit filter compact filter van Cittert deconvolution method signal analysis sub-filter scales reconstruction Large Eddy Simulation

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Archives of Mechanics

Rocznik

2023

Tom

Vol. 75, nr 1-2

Strony

107--149

Opis fizyczny

Bibliogr. 93 poz., tab., wykr.

Twórcy

autor

Caban L.

Department of Thermal Machinery, Czestochowa University of Technology, Faculty of Mechanical Engineering and Computer Science, Armii Krajowej 21, 42-201 Czestochowa, Poland

autor

Tyliszczak A.

artur.tyliszczak@pcz.pl

Department of Thermal Machinery, Czestochowa University of Technology, Faculty of Mechanical Engineering and Computer Science, Armii Krajowej 21, 42-201 Czestochowa, Poland

Bibliografia

1. R. Vichnevetsky, J.B. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations, SIAM, Philadelphia, 1982.
2. R. Bracewell, J. Roberts, Aerial smoothing in radio astronomy, Australian Journal of Physics, 7, 4, 615, 1954.
3. P.H. Van Cittert, Zum Einflußder Spaltbreite auf die Intensitätsverteilung in Spektrallinien, II. Zeitschrift Für Physik, 69, 5-6, 298–308, 1931.
4. H.C. Burger, P.H. van Cittert, Wahre und scheinbare Intensitätsverteilung in Spektrallinien, Zeitschrift Für Physik, 79, 11-12, 722–730, 1932.
5. M.G. Smith, A.N. Walker, Correction of observational profiles of spectral lines, Astrophysics and Space Science, 1, 2, 151–165, 1968.
6. A.R. Stokes, A numerical Fourier-analysis method for the correction of widths and shapes of lines on X-ray powder photographs, Proceedings of the Physical Society, 61, 4, 382–391, 1948.
7. M.S. Paterson, Calculation of the correction for instrumental broadening in X-ray diffraction lines, Proceedings of the Physical Society, Section A, 63, 5, 477–482, 1950.
8. S. Ergun, Direct method for unfolding convolution products – its application to X-ray scattering intensities, Journal of Applied Crystallography, 1, 1, 19–23, 1968.
9. P.A. Jansson, Method for determining the response function of a high-resolution infrared spectrometer, Journal of the Optical Society of America, 60, 2, 184–191, 1970.
10. P. Jansson, Deconvolution with Applications in Spectroscopy, Academic Press, New York, 1984.
11. F. Yano, S. Nomura, Deconvolution of scanning electron microscopy images, Scanning, 15, 1, 19–24, 1993.
12. E.J. Rapperport, Deconvolution: A Technique to Increase Electron Probe Resolution, [in:] Electron Probe Microanalysis, A.J. Tousimis and L. Marton [eds.], Academic Press, New York, p. 117, 1969.
13. Z. Mencik, Iterative deconvolution of smeared data functions, Journal of Applied Crystallography, 7, 1, 44–50, 1974.
14. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging, Bristol, U.K.: IOP, 1998.
15. L. Wang, Y. Huang, X. Luo, Z. Wang, S. Luo, Image deblurring with filters learned by extreme learning machine, Neurocomputing, 74, 16, 2464–2474, 2011.
16. S. Kawata, Y. Ichioka, Iterative image restoration for linearly degraded images I Basis, Journal of the Optical Society of America, 70, 7, 762, 1980.
17. S. Kawata, Y. Ichioka, Iterative image restoration for linearly degraded images II Reblurring procedure, Journal of the Optical Society of America, 70, 7, 768, 1980.
18. H.J. Scudder, Introduction to computer aided tomography, Proceedings of the IEEE, 66, 6, 628–637, 1978.
19. Z. Danovich, Y. Segal, Laminogram reconstruction through regularizing Fourier filtration, NDT and E International, 27, 3, 123–130, 1994.
20. Y. Ge, Q. Zhang, Z. Hu, J. Chen, W. Shi, H. Zheng, D. Liang, Deconvolutionbased backproject-filter (BPF) computed tomography image reconstruction method using deep learning technique, arXiv preprint: arXiv:1807.01833, 2018.
21. Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature, 521, 436–444, 2015.
22. K.H. Jin, M.T. McCann, E. Froustey, M. Unser, Deep convolutional neural network for inverse problems in imaging, IEEE Transactions on Image Processing, 26, 9, 4509–4522, 2017.
23. S. Haykin, Blind Deconvolution, PTR Prentice Hall, 1994.
24. P. Campisi, K. Egiazarian, Blind Image Deconvolution. Theory and Applications, CRC Press, 2007.
25. M.S.C. Almeida, L.B. Almeida, Blind and Semi-Blind Deblurring of Natural Images, IEEE Transactions on Image Processing, 19, 1, 36–52, 2010.
26. S. Jefferies, K. Schulze, C. Matson, K. Stoltenberg, E.K. Hege, Blind deconvolution in optical diffusion tomography, Optics Express, 10, 1, 46, 2002.
27. C. Yu, C. Zhang, L. Xie, A blind deconvolution approach to ultrasound imaging, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59, 2, 271–280, 2012.
28. T. Taxt, G.V. Frolova, Noise robust one-dimensional blind deconvolution of medical ultrasound images, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 46, 2, 291–299, 1999.
29. T. Taxt, J. Strand, Two-dimensional noise-robust blind deconvolution of ultrasound images, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 48, 4, 861–866, 2001.
30. T. Taxt, Three-dimensional blind deconvolution of ultrasound images, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 48, 4, 867–871, 2001.
31. R. Grüner, T. Taxt, Iterative blind deconvolution in magnetic resonance brain perfusion imaging, Magnetic Resonance in Medicine, 55, 4, 805–815, 2006.
32. J. Ma, F.-X. Le Dimet, Deblurring from highly incomplete measurements for remote sensing, IEEE Transactions on Geoscience and Remote Sensing, 47, 3, 792–802, 2009.
33. M.J. Roan, M.R. Gramann, J.G. Erling, L.H. Sibul, Blind deconvolution applied to acoustical systems identification with supporting experimental results, The Journal of the Acoustical Society of America, 114, 4, 1988–1996, 2003.
34. T.G. Stockham, T.M. Cannon, R.B. Ingebretsen, Blind deconvolution through digital signal processing, Proceedings of the IEEE, 63, 4, 678–692, 1975.
35. G.T. Zheng, M.A. Buckley, G. Kister, G.F. Fernando, Blind deconvolution of acoustic emission signals for damage identification in composites, AIAA Journal, 39, 6, 1198–1205, 2001.
36. T. Yamaguchi, T. Mizutani, M. Tarumi, D. Su, Sensitive damage detection of reinforced concrete bridge slab by “Time-Variant Deconvolution” of SHF-Band Radar Signal, IEEE Transactions on Geoscience and Remote Sensing, 1–11, 2018.
37. A.K. Takahata, E.Z. Nadalin, R. Ferrari, L.T. Duarte, R. Suyama, R.R. Lopes, J.M.T.Romano, M. Tygel, Unsupervised processing of geophysical signals: a review of some key aspects of blind deconvolution and blind source separation, IEEE Signal Processing Magazine, 29, 4, 27–35, 2012.
38. Y. Li, G. Zhang, A seismic blind deconvolution algorithm based on bayesian compressive sensing, Mathematical Problems in Engineering, 2015, 1–11, 2015.
39. M. Mirel, I. Cohen, Multichannel semi-blind deconvolution (MSBD) of seismic signals, Signal Processing, 135, 253–262, 2017.
40. H.-Z. Wu, L.-Y. Fu, X.-H. Meng, Blind deconvolution of seismic signals with non-white reflectivities, Exploration Geophysics, 38, 4, 235–241, 2007.
41. H.H. Lari, A. Gholami, Nonstationary blind deconvolution of seismic records, Geophysics, 84, 1, V1–V9, 2019.
42. P. Castaldi, R. Diversi, R.P. Guidorzi, U. Soverini, Blind estimation and deconvolution of communication channels with unbalanced noise, IFAC Proceedings Volumes, 33, 15, 325–330, 2000.
43. S. Cang, J. Swärd, X. Sheng, A. Jakobsson, Toeplitz-based blind deconvolution of underwater acoustic channels using wideband integrated dictionaries, Signal Processing, 107812, 2020.
44. W.J. Layton, L.G. Rebholz, Approximate Deconvolution Models of Turbulence, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, 2012.
45. F.K. Chow, R.L. Street, M. Xue, J.H. Ferziger, Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow, Journal of the Atmospheric Sciences, 62, 7, 2058–2077, 2005.
46. J. Mathew, R. Lechner, H. Foysi, J. Sesterhenn, R. Friedrich, An explicit filtering method for large eddy simulation of compressible flows, Physics of Fluids, 15, 8, 2279–2289, 2003.
47. J. Gullbrand, F.K. Chow, The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering, Journal of Fluid Mechanics, 495, 323–341, 2003.
48. D. Carati, G. S. Winckelmans, H. Jeanmart, On the modelling of the sub-grid-scale and filtered-scale stress tensors in large-eddy simulation, Journal of Fluid Mechanics, 441, 119–138, 2001.
49. B.J. Geurts, F. van der Bos, Numerically induced high-pass dynamics in large-eddy simulation, Physics of Fluids, 17, 12, 125103, 2005.
50. S. Stolz, N.A. Adams, An approximate deconvolution procedure for large-eddy simulation, Physics of Fluids, 11, 7, 1699–1701, 1999.
51. S. Stolz, N.A. Adams, L. Kleiser, An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows, Physics of Fluids, 13, 4, 997–1015, 2001.
52. J.A. Domaradzki, N.A. Adams, Direct modelling of sub-grid scales of turbulence in large eddy simulations, Journal of Turbulence, 3, N24, 2002.
53. P. Schlatter, S. Stolz, L. Kleiser, LES of transitional flows using the approximate deconvolution model, International Journal of Heat and Fluid Flow, 25, 3, 549–558, 2004.
54. O.A. Mahfoze, S. Laizet, Non-explicit large eddy simulations of turbulent channel flows from Re_ = 180 up to Re_ = 5200, Computers and Fluids, 228, 105019, 2021.
55. S. Stolz, N.A. Adams, L. Kleiser, The approximate deconvolution model for largeeddy simulations of compressible flows and its application to shock-turbulent-boundarylayer interaction, Physics of Fluids, 13, 10, 2985–3001, 2001.
56. R. Von Kaenel, N.A. Adams, L. Kleiser, J. Vos, An approximate deconvolution model for large-eddy simulation of compressible flows with finite-volume schemes, 40th AIAA Aerospace Sciences Meeting and Exhibit, 2002.
57. N.A. Adams, A. Stolz, A sub-grid-Scale Deconvolution Approach for Shock Capturing, Journal of Computational Physics, 178, 391–426, 2002.
58. L. Goodfriend, F.K. Chow, M. Vanella, E. Balaras, Large-eddy simulation of decaying isotropic turbulence across a grid refinement interface using explicit filtering and reconstruction, Journal of Turbulence, 14, 12, 58–76, 2013.
59. O. San, A.E. Staples, T. Iliescu, A posteriori analysis of low-pass spatial filters for approximate deconvolution LES of homogeneous incompressible flows, International Journal of Computational Fluid Dynamics, 29, 1, 40–66, 2014.
60. O. San, Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence, International Journal of Computational Fluid Dynamics, 30, 1, 20–37, 2016.
61. O. San, P. Vedula, Generalized Deconvolution Procedure for Structural Modeling of Turbulence, Journal of Scientific Computing, 75, 2, 1187–1206, 2017.
62. O. San, A.E. Staples, Z. Wang, T. Iliescu, Approximate deconvolution large eddy simulation of a barotropic ocean circulation model, Ocean Modelling, 40, 2, 120–132, 2011.
63. O. San, A.E. Staples, T. Iliescu, Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model, Ocean Modelling, 63, 1–20, 2013.
64. F.K. Chow, R.L. Street, M. Xue, J.H. Ferziger, Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow, Journal of the Atmospheric Sciences, 62, 7, 2058–2077, 2005.
65. F.K. Chow, R.L. Street, Evaluation of turbulence closure models for large-eddy simulation over complex terrain: flow over Askervein hill, Journal of Applied Meteorology and Climatology, 48, 5, 1050–1065, 2009.
66. B. Zhou, F.K. Chow, Large-eddy simulation of the stable boundary layer with explicit filtering and reconstruction turbulence modeling, Journal of the Atmospheric Sciences, 68, 9, 2142–2155, 2011.
67. P. Domingo, L. Vervisch, Large eddy simulation of premixed turbulent combustion using approximate deconvolution and explicit flame filtering, Proceedings of the Combustion Institute, 35, 2, 1349–1357, 2015.
68. Q.Wang, M. Ihme, Regularized deconvolution method for turbulent combustion modeling, Combustion and Flame, 176, 125–142, 2017.
69. C. Mehl, J. Idier, B. Fiorina, Evaluation of deconvolution modelling applied to numerical combustion, Combustion Theory and Modelling, 22, 1, 38–70, 2017.
70. C.D. Pruett, B.C. Thomas, C.E. Grosch, T.B. Gatski, A temporal approximate deconvolution model for large-eddy simulation, Physics of Fluids, 18, 2, 028104, 2006.
71. J. Borggaard, T. Iliescu, Approximate deconvolution boundary conditions for large eddy simulation, Applied Mathematics Letters, 19, 8, 735–740, 2006
72. P. Schlatter, Large-eddy simulation of transition and turbulence in wall-bounded shear flow, PhD Thesis, ETH Zurich, 2005.
73. A.A. Dunca, R. Lewandowski, Modeling error in approximate deconvolution models, Communications in Mathematical Sciences, 12, 4, 757–778, 2014.
74. A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, V.H. Winston and Sons, Washington, DC, 1977.
75. C. Eckart, The correction of continuous spectra for the finite resolution of the spectrometer, Physical Review, 51, 9, 735–738, 1937.
76. T. Sarkar, D. Weiner, V. Jain, Some mathematical considerations in dealing with the inverse problem, IEEE Transactions on Antennas and Propagation, 29, 2, 373–379, 1981.
77. M. Ekstrom, A spectral characterization of the ill-conditioning in numerical deconvolution, IEEE Transactions on Audio and Electroacoustics, 21, 4, 344–348, 1973.
78. R. Gold, An Iterative Unfolding Method for Response Matrices, Mathematics and Computer Research and Development Rep. ANL-6984, Argonne National Laboratory, Argonne, III, 1964.
79. S. Singh, S.N Tandon, H.M. Gupta, An iterative restoration technique, Signal Processing, 11, 1, 1–11, 1986.
80. G. Thomas, An improvement of the Van-Cittert’s method, ICASSP’81, IEEE International Conference on Acoustics, Speech, and Signal Processing, 1981.
81. N.R. Hill, G.E. Ioup, Convergence of the van Cittert iterative method of deconvolution, Journal of the Optical Society of America, 66, 5, 487, 1976.
82. B. Parruck, S.M. Riad, An optimization criterion for iterative deconvolution, IEEE Transactions on Instrumentation and Measurement, 32, 1, 137–140, 1983.
83. A. Bennia, S.M. Riad, Filtering capabilities and convergence of the Van-Cittert deconvolution technique, IEEE Transactions on Instrumentation and Measurement, 41, 2, 246–250, 1992.
84. S.K. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, 103, 1, 16–42, 1992.
85. D.V. Gaitonde, J.S. Shang, J.L. Young, Practical aspects of higher-order numerical schemes for wave propagation phenomena, Internationa Journal of Numerical Methods in Engeeniring, 45, 1849, 1999.
86. P. Sagaut, Large Eddy Simulation for Incompressible Flows, Springer-Verlag, Berlin, Heidelberg, 2001.
87. B.J. Geurts, Elements of Direct and Large-Eddy Simulation, Edwards Publishing, Dordrecht, 2004.
88. O. San, A.E. Staples, High-order methods for decaying two-dimensional homogeneous isotropic turbulence, Computers and Fluids, 63, 105–127, 2012.
89. L. Caban, A. Tyliszczak, High-order compact difference schemes on wide computational stencils with a spectral-like accuracy, Computers and Mathematics with Applications, 108, 123–140, 2022.
90. W. Layton, R. Lewandowski, A simple and stable scale-similarity for large eddy simulation: energy and existence of weak solutions, Applied Mathematics Letters, 16, 1205–1209, 2003.
91. A. Dunca, Y. Epshteyn, On the Stolz-Adams deconvolution model for large eddy simulation of turbulent flows, SIAM Journal of Mathematical Analysis, 37, 6, 1890–1902, 2006.
92. L.C. Berselli, R. Lewandowski, Convergence of approximate deconvolution models to the mean Navier–Stokes equations, L’Association Publications de l’Institut Henri Poincaré, 29, 171–198, 2012.
93. C. Canuto, M.Y. Hussaini, A. Quarteroni, T. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, Heidelberg, 1998.

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-95ac797d-cd54-41b0-ab6f-323a1fca1e5a