{"id":26437259,"url":"https://github.com/zolabar/conformalmappingsympy","last_synced_at":"2025-10-25T04:40:13.936Z","repository":{"id":129366710,"uuid":"370634569","full_name":"zolabar/ConformalMappingSympy","owner":"zolabar","description":"This repository hosts code that illustrates the content of the presentation and proceeding Conformal Mappings with Sympy: Towards Python-driven Analytical Modeling in Physics a collaborative work of Z. Lauer-Baré and E. Gaertig presented on THE 20th PYTHON IN SCIENCE CONF. 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(SCIPY 2021)](https://www.scipy2021.scipy.org/).\n\nPython scripts and Jupyter notebooks are provided.\n\nPlease refer to \n\nLauer-Baré Z. and Gaertig E., [*Conformal Mappings with SymPy: Towards Python-driven Analytical Modeling in Physics*. Lauer-Baré, Z. \u0026 Gaertig, E. In Agarwal, M., Calloway, C., Niederhut, D., \u0026 Shupe, D., editors, Proceedings of the 20th Python in Science Conference, pages 85 - 93, 2021. ](https://conference.scipy.org/proceedings/scipy2021/lauer_bare_gaertig.html)\n\nwhen using formulae, code, figures or animations from this repository. The conference talk can be seen on the [Enthought YouTube channel](https://www.youtube.com/watch?v=P5ybpjv2uDA).\n\nThe theoretical methods used here are conformal mappings, inspired by [PHW33](https://www.tandfonline.com/doi/abs/10.1080/14786443309462212) and [BC09](https://www.mheducation.com/highered/product/complex-variables-applications-brown-churchill/M9780073383170.html) and Taylor-expansions, following [LGK21](https://journals.riverpublishers.com/index.php/IJFP/article/view/5535) and [LGKS23](https://publications.rwth-aachen.de/record/957191). These methods are used to solve the Stokes problem in an eccentric annular domain for Couette-Poiseuille flow and to calculate the corresponding flow force in a postprocessing step, as well as analyzing the limits for small gaps. The context of this work is the modelling of viscous fluid power systems (see [LGK21](https://journals.riverpublishers.com/index.php/IJFP/article/view/5535) for more details).\n\nApplications of conformal mappings with SymPy in the context of inviscid irrotational flow can be found on [Plotting streamlines with Matplotlib and SymPy](https://tonysyu.github.io/plotting-streamlines-with-matplotlib-and-sympy.html#.YPf_rKjwhPb) (T. S. Yu).\nFurther applications of conformal mappings with SymPy in the context of inviscid irrotational flow applied to naval engineering are described in [G21](https://www.mdpi.com/2077-1312/9/2/108) with an open Python code repository in [naval Python and SymPy](https://zenodo.org/record/4452633#.YPpnYegzZPZ).\n\nFurther, a Python package with cloud computing possibility via binder, for visualizing conformal mappings interactively, based on SymPy, NumPy and Plotly can be found at the page  [conformalMaps](https://github.com/im-AMS/Conformal-Maps); see [LA21](https://doi.org/10.5281/zenodo.5717868).\n\n## Transformation of eccentric annulus to concentric annulus\n\n```code_block_moebius.py``` and ```moebius.ipynb``` with a Möbius transform of the type\n\n\u003cimg src=\"https://render.githubusercontent.com/render/math?math=w(z)=\\frac{z %2B ia}{az %2B i}\"\u003e\n\nThe following animation was created with an adapted version of the code from [the interactive Python code for conformal mappings mentioned above](https://github.com/im-AMS/Conformal-Maps), where the results from [LG21](https://conference.scipy.org/proceedings/scipy2021/lauer_bare_gaertig.html) were implemented.\n\n[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/zolabar/Conformal-Maps/HEAD)\n![](Figures/moebius.gif)\n\n## Transformation of eccentric annulus to rectangle\n\n```code_block_bipolar.py``` and ```bipolar.ipynb``` with a conformal mapping related to bipolar coordinates\n\n\u003cimg src=\"https://render.githubusercontent.com/render/math?math=w(z)=2\\cdot \\tan^{-1}\\left(\\frac{z %2B i\\gamma}{c}\\right)\"\u003e\n\nThe following animation was created with an adapted version of the code from [the interactive Python code for conformal mappings mentioned above](https://github.com/im-AMS/Conformal-Maps), where the results from [LG21](https://conference.scipy.org/proceedings/scipy2021/lauer_bare_gaertig.html) were implemented.\n\n[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/zolabar/Conformal-Maps/HEAD)\n![](Figures/mapping_arctan_colored_boundary.gif)\n\n## Postprocessing\n\nThe postprocessing is shown in the file ```moebius.ipynb``` , due to LaTeX rendering of web browser based *Jupyter notebook*.\n\nFlow force calculation with ```diff``` and Taylor expansion of force in the gap \n\n\u003cimg src=\"https://render.githubusercontent.com/render/math?math=\\delta\"\u003e\n\nwith ```series```.\n\n## Literature\n\n[BC09] [Brown J.W., Churchill R.V., Complex variables and applications, Eighth edition, McGraw-Hill Book Company; 2009](https://www.mheducation.com/highered/product/complex-variables-applications-brown-churchill/M9780073383170.html)\n\n[G21] [Grm, A., Ships Added Mass Effect on a Flexible Mooring Dolphin in Berthing Manoeuvre. J. Mar. Sci. Eng. 2021, 9, 108. https://doi.org/10.3390/jmse9020108](https://www.mdpi.com/2077-1312/9/2/108)\n\n[LGK21] [Lauer-Baré Z., Gaertig E., Krebs J., Arndt C., Sleziona C., Gensel A., A note on leakage jet forces: Application in the modelling of digital twins of hydraulic valves, International Journal of Fluid Power, 2021, Vol. 22 (1), 113–146](https://journals.riverpublishers.com/index.php/IJFP/article/view/5535)\n\n[LGKS23] [Lauer-Baré Z., Gaertig E., Krebs J., Sleziona C. Analytical formulae in fluid power, quo vadis in times of CFD and I4.0? 13th International Fluid Power Conference, p. 866-879, 2023](https://publications.rwth-aachen.de/record/957191)\n\n[LG21] Lauer-Baré Z. and Gaertig E., [*Conformal Mappings with SymPy: Towards Python-driven Analytical Modeling in Physics*. Lauer-Baré, Z. \u0026 Gaertig, E. In Agarwal, M., Calloway, C., Niederhut, D., \u0026 Shupe, D., editors, Proceedings of the 20th Python in Science Conference, pages 85 - 93, 2021. ](https://conference.scipy.org/proceedings/scipy2021/lauer_bare_gaertig.html)\n\n[LA21] Lauer-Baré Z. and Aditya, [*Conformal-Maps: Code for interactive conformal mapping with python and jupyter notebook* (v1.0.1). Zenodo. 2021 https://doi.org/10.5281/zenodo.5717868.](https://doi.org/10.5281/zenodo.5717868)\n\n[PHW33] [Piercy N.A.V., Hooper M.S., Winny H.F., LIII. Viscous flow through pipes with cores, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1933](https://www.tandfonline.com/doi/abs/10.1080/14786443309462212)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzolabar%2Fconformalmappingsympy","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fzolabar%2Fconformalmappingsympy","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzolabar%2Fconformalmappingsympy/lists"}