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Numerical methods in fluid mechanics – an overview

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The article presents in a review way the most important numerical methods used in modern fluid mechanics. The individual chapters discuss Finite Difference Method, Finite Volume Method, Lattice Boltzmann Method, Discrete Element Method and Smoothed Particle Hydrodynamics. The aim of the article is to familiarize the reader with the most important concepts, features and mathematical equations used in particular methods. The article is intended mainly for people who want to get acquainted with the current possibilities of numerical modelling in the field of broadly understood fluid mechanics. The material is intended to facilitate the decision on how to implement the planned play research.
Słowa kluczowe
Rocznik
Tom
Strony
185--218
Opis fizyczny
Bibliogr. 54 poz., rys., wykr.
Twórcy
  • Katedra Mechaniki i Podstaw Konstrukcji Maszyn, Uniwersytet Warmińsko-Mazurski, ul. Oczapowskiego 11, 10-736 Olsztyn
  • Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia
Bibliografia
  • ABAS A., MOKHTAR N.H., ISHAK H.H.H., ABDULLAH M.Z., TIAN A.H. 2016. Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem. Computational and Mathematical Methods in Medicine, 2016, article ID 6143126. https://doi.org/10.1155/2016/6143126
  • ARCHAMBEAU P., PIROTTON M., DEWALS B., DUCHÊNE L., MOUZELARD T. 2013. Development of a didactic SPH model. Université de Liège - Faculté des Sciences Appliquées.
  • BHATNAGAR P.L., GROSS E.P., KROOK M. 1954. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Physical Review, 94: 511-525.
  • BUI H.H., NGUYEN G.D. 2021. Smoothed particle hydrodynamics (SPH) and its applications in geomechanics: From solid fracture to granular behaviour and multiphase flows in porous media. Computers and Geotechnics, 138: 104315.
  • BURDEN R.L., FAIRES J.D. 2011. Numerical Analysis. 9th Edition. Brooks/Cole, Pacific Grove.
  • CAUSON D.M., MINGHAM C.G. 2010. Introductory Finite Difference Methods for PDEs. Ventus Publishing ApS.
  • CHU K. 2010. CFD-DEM simulation of complex particle-fluid flows. PhD Thesis. The University of New South Wales.
  • COURANT R., FRIEDRICHS K., LEWY H. 1928. On the Partial Difference Equations of Mathematical Physics. Mathematische Annalen, 100: 32-74.
  • CUNDALL P., STRACK O. 1979. A discrete element model for granular assemblies. Géotechnique, 29: 47-65.
  • DOUILLET-GRELLIER T., JONES B.D, PRAMANIK R., PAN K., ALBAIZ A., WILLIAMS J.R. 2016. Mixed-mode fracture modeling with smoothed particle hydrodynamics. Computers and Geotechnics, 79: 73-85.
  • FULCHINI F., GHADIRI M., BORISSOVA A., AMBLARD B., BERTHOLIN S., CLOUPET A., YAZDANPANAH M. 2019. Development of a methodology for predicting particle attrition in a cyclone by CFD-DEM. Powder Technology, 357: 21-32.
  • GAO Y., CHENG Y, CHEN J. 2023. Experimental Study and 3-D Meso-Scale Discrete Element Modeling on the Compressive Behavior of Foamed Concrete. Buildings, 13: 674.
  • GESTEIRA M.G., ROGERS B.B, DALRYMPLE R.A., CRESPO A.J.C., NARAYANASWAMY M. 2010. User Guide for the SPHysics code. Retrieved from https://wiki.manchester.ac.uk/sphysics/index.php/SPHYSICS_Home_Page (20.05.2023).
  • GOFFIN L. 2013. Development of a didactic SPH model. MSc Thesis, Université de Ličge (Belgium).
  • HERTZ H. 1881. Über die berührung fester elastischer Körper. Journal für die Reine und Angewandte Mathematik, 92: 156-171.
  • HUGHES T.J.R., ZIENKIEWICZ O.C. 1979. Finite elements in fluid mechanics: an introduction to the Galerkin method. Pergamon Press, Oxford.
  • IYENGAR S.R.K., JAIN R.K. 2009. Numerical Methods. New Age International Publishers, New Delhi.
  • KHAN S.A., KOÇ M. 2022. Numerical modelling and simulation for extrusion-based 3D concrete printing: The underlying physics, potential, and challenges. Results in Materials, 16: 100337.
  • KORN Ch., HERLITZIUS T. 2012. Coupled CFD-DEM simulation of separation process in combine harvester cleaning devices. Landtechnik, 72(5): 247-261.
  • KOUKOUVINIS P., KYRIAZIS N., GAVAISES M. 2018. Smoothed particle hydrodynamics simulation of a laser pulse impact onto a liquid metal droplet. PLoS ONE, 13(9): e0204125.
  • KRAUSE M.J. 2010. Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers – Application to the Human Respiratory System. PhD Thesis. Karlsruhe Institute of Technology.
  • KRÜGER T., KUSUMAATMAJA H., KUZMIN A., SHARDT O., SILVA G., VIGGEN E.M. 2017. The Lattice Boltzmann Method – Principles and Practice. Springer, Berlin.
  • LABRA C.A, ONATE E., ROJEK J. 2012. Advances in the development of the discrete element method for excavation processes. Monograph CIMNE, Nº-132: 1-213.
  • LANGTANGEN H.P., LINGE S. 2017. Finite Difference Computing with PDEs – A Modern Software Approach. Springer Open, Berlin.
  • LI S., LIU W.K. 2007. Meshfree Particle Methods. Springer, Berlin.
  • LIND S.J., ROGERS B.D., STANSBY P.K. 2020. Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2241).
  • LIU G.R., LIU M.B. 2003. Smoothed Particle Hydrodynamics. Word Scientific Publishing, Singapore.
  • LIU Z., MA H., ZHAO Y. 2021. CFD-DEM Simulation of Fluidization of Polyhedral Particles in a Fluidized Bed. Energies, 14: 4939.
  • MACCORMACK R.W., PAULLAY A.J. 1972. Computational efficiency achieved by time splitting of finite difference operators. AIAA Paper, 72-154, San Diego.
  • MCDONALD P.W. 1971. The Computation of Transonic Flow Through Two-Dimensional Gas Turbine Cascades. Proceedings of the ASME 1971 International Gas Turbine Conference and Products Show. ASME 1971 International Gas Turbine Conference and Products Show, Houston, Texas, USA. March 28-April 1.
  • MENTER F.R. 1993. Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows. AIAA Paper, 93-2906.
  • MOHAMAD A.A. 2011. Lattice Boltzmann Method. Fundamentals and Engineering Applications with Computer Codes. Springer, Berlin.
  • MOUKALLED F., MANGANI F., DARWISH M. 2016. The Finite Volume Method in Computational Fluid Dynamics. Springer, Berlin.
  • NGUYEN T.T.T., HOJNY M. 2022. Application of Smoothed Particle Hydrodynamics Method in Metal Processing: An Overview. Archives of Foundry Engineering, 3: 67-80.
  • NIEDŹWIEDZKA A., SCHNERR G.H., SOBIESKI W. 2016. Review of numerical models of cavitating flows with the use of the homogeneous approach. Archives of Thermodynamics, 37(2): 71-88.
  • ORSZAG S.A. 1970. Analytical Theories of Turbulence. Journal of Fluid Mechanics, 41: 363-386.
  • PESKIN C.S. 1977. Numerical Analysis of Blood Flow in the Heart. Journal of Computational Physics, 25: 220-252.
  • PLATZER F., FIMBINGER E. 2021. Modelling Pasty Material Behaviour Using the Discrete Element Method. Multiscale Science and Engineering, 3: 119-128.
  • SCHUBIGER A., BARBER S., NORDBORG H. 2020. Evaluation of the lattice Boltzmann method for wind modelling in complex terrain. Wind Energy Science, 5: 1507-1519.
  • SOBIESKI W. 2009. Switch function and sphericity coefficient in the Gidaspow drag model for modeling solid-fluid systems. Drying Technology, 27(2): 267-280.
  • SOBIESKI W., GRYGO D. 2019. Fluid flow in the impulse valve of a hydraulic ram. Technical Sciences, 22(3): 205-220.
  • SOBIESKI W., MATYKA M., GOŁEMBIEWSKI J., LIPIŃSKI S. 2018. The Path Tracking Method as an alternative for tortuosity determination in granular beds. Granular Matter, 20: 72.
  • SMAGORINSKY J. 1963. General circulation experiments with the primitive equations I. the basic experiment. Monthly Weather Review, 91(3): 99-164.
  • SPALART P.R. 1997. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In Proceedings of first AFOSR international conference on DNS/LES, Greyden Press.
  • SUCCI S. 2001. The Latttice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon Press, Oxford.
  • SUKOP M.C., THORNE D.T. 2006. Lattice Boltzmann Modeling - An Introduction for Geoscientists and Engineers. Springer, Berlin.
  • The YADE code. Retrieved from https://yade-dem.org/doc/ (20.05.2023).
  • TRUSHNIKOV D.N., KOLEVA E.G., DAVLYATSHIN R.P., GERASIMOV R.M., BAYANDIN Y.V. 2019. Mathematical modeling of the electronbeam wire deposition additive manufacturing by the smoothed particle hydrodynamics method. Mechanics of Advanced Materials and Modern Processes, 5: 4.
  • URLICH Ch. 2013. Smoothed-Particle-Hydrodynamics Simulation of Port Hydrodynamic Problems. TUHH, Hamburg.
  • WAGNER A.J. 2008. A Practical Introduction to the Lattice Boltzmann Method. North Dakota State University, Fargo.
  • WEINAN E., LIU J.-G. 2000. Gauge finite element method for incompressible flows. International Journal for Numerical Methods in Fluids, 24(8): 701-710.
  • XIE Y., LIU Y., LI L., XU Ch., LI B. 2018. Simulation of different gas-solid flow regimes using a drag law derived from lattice Boltzmann simulations. The Journal of Computational Multiphase Flows, 10(4): 202-2014.
  • ZIENKIEWICZ O.C., TAYLOR R.L., NITHIARASU P. 2005. The Finite Element Method for Fluid Dynamics. Butterworth-Heinemann, Oxford (UK).
  • ZOU Y., CHEN Ch., ZHANG L. 2020. Simulating Progression of Internal Erosion in Gap-Graded Sandy Gravels Using Coupled CFD-DEM. International Journal of Geomechanics, 20(1): 04019135-1.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dc57c33f-a863-442f-9fae-0c0181f0095a
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