A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions
We consider flows of an incompressible Navier–Stokes fluid in a tubular domain with Navier’s slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed fi...
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| Published in | Applications in engineering science Vol. 6; p. 100038 |
|---|---|
| Main Authors | , , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2021
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2666-4968 2666-4968 |
| DOI | 10.1016/j.apples.2021.100038 |
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| Abstract | We consider flows of an incompressible Navier–Stokes fluid in a tubular domain with Navier’s slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark.
Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries. |
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| AbstractList | We consider flows of an incompressible Navier-Stokes fluid in a tubular domain with Navier's slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries. We consider flows of an incompressible Navier–Stokes fluid in a tubular domain with Navier’s slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries. |
| ArticleNumber | 100038 |
| Author | Švihlová, H. Chabiniok, R. Hron, J. Málek, J. Jarolímová, A. Rajagopal, K. Tůma, K. Rajagopal, K.R. |
| Author_xml | – sequence: 1 givenname: R. orcidid: 0000-0002-7527-2751 surname: Chabiniok fullname: Chabiniok, R. email: radomir.chabiniok@inria.fr organization: Inria Saclay Ile-de-France, 1 Rue Honoré d’Estienne d’Orves, Palaiseau 91120, France – sequence: 2 givenname: J. orcidid: 0000-0001-5862-2353 surname: Hron fullname: Hron, J. email: jaroslav.hron@mff.cuni.cz organization: Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic – sequence: 3 givenname: A. orcidid: 0000-0003-2704-2211 surname: Jarolímová fullname: Jarolímová, A. organization: Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic – sequence: 4 givenname: J. surname: Málek fullname: Málek, J. email: josef.malek@mff.cuni.cz organization: Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic – sequence: 5 givenname: K.R. surname: Rajagopal fullname: Rajagopal, K.R. email: krajagopal@tamu.edu organization: Texas A&M University, Department of Mechanical Engineering, College Station, TX 77843-3132, United States – sequence: 6 givenname: K. surname: Rajagopal fullname: Rajagopal, K. email: keshava.rajagopal@gmail.com organization: University of Houston College of Medicine and Houston Heart / HCA Houston Healthcare, Houston, Texas, United States – sequence: 7 givenname: H. surname: Švihlová fullname: Švihlová, H. email: helena.svihlova@mff.cuni.cz organization: Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic – sequence: 8 givenname: K. surname: Tůma fullname: Tůma, K. email: ktuma@karlin.mff.cuni.cz organization: Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic |
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| References | Sime, N., Wilson, C. R., 2020. Automatic weak imposition of free slip boundary conditions via Nitsche’s method: application to nonlinear problems in geodynamics. Juntunen, Stenberg (bib0017) 2009; 78 Abhyankar, S., Brown, J., Constantinescu, E. M., Ghosh, D., Smith, B. F., Zhang, H., 2018. PETSc/TS: A Modern Scalable ODE/DAE Solver Library. Navier (bib0022) 1823; 6 Neto, Evans, Bonaccurso, Butt, Craig (bib0023) 2005; 68 Babuška (bib0003) 1959; 39 Poisson (bib0027) 1831; 13 Stokes, Carey (bib0033) 2011; 21 Engelman, Sani, Gresho (bib0014) 1982; 2 Womersley (bib0039) 1955; 127 Balay, Abhyankar, Adams, Brown, Brune, Buschelman, Dalcin, Dener, Eijkhout, Gropp, Karpeyev, Kaushik, Knepley, May, McInnes, Mills, Munson, Rupp, Sanan, Smith, Zampini, Zhang, Zhang (bib0004) 2020 Layton (bib0018) 1999; 38 Girard (bib0015) 1813 Nubar (bib0026) 1971; 11 de Prony, G.C.F.M.R.B. (bib0028) 1804 Madukauwa-David, Midha, Sharma, McLain, Mitra, Crawford, Yoon, Makkar, Yoganathan (bib0019) 2018; 93 Urquiza, Garon, Farinas (bib0035) 2014; 256 Alnæs, Blechta, Hake, Johansson, Kehlet, Logg, Richardson, Ring, Rognes, Wells (bib0002) 2015; 3 Hron, Roux, Málek, Rajagopal (bib0016) 2008; 56 Braack, Mucha (bib0008) 2014; 32 Becker, Capatina, Luce, Trujillo (bib0005) 2015; 295 Rieder (bib0030) 1974; 1 Nubar (bib0025) 1967; 4 Bugliarello, Hayden (bib0009) 1963; 7 Wieners (bib0038) 2003 de Coulomb (bib0011) 1800; 3 Stokes (bib0032) 1845; 8 Verfürth (bib0037) 1991; 59 Dione, Tibirna, Urquiza (bib0012) 2013; 27 Boffi, Brezzi, Fortin (bib0007) 2013 Verfürth (bib0036) 1986; 50 Mekhlouf, Baggag, Remaki (bib0020) 2017; 4 Rajagopal, Rajagopal (bib0029) 2020; 8 Švihlová, Hron, Málek, Rajagopal, Rajagopal (bib0034) 2017; 114 Burman (bib0010) 2012; 50 Misra, Shit (bib0021) 2007; 07 Du Buat (bib0013) 1786 Nitsche (bib0024) 1971; 36 Bennett (bib0006) 1967; 155 Becker (10.1016/j.apples.2021.100038_bib0005) 2015; 295 de Coulomb (10.1016/j.apples.2021.100038_bib0011) 1800; 3 Layton (10.1016/j.apples.2021.100038_bib0018) 1999; 38 Wieners (10.1016/j.apples.2021.100038_bib0038) 2003 Engelman (10.1016/j.apples.2021.100038_bib0014) 1982; 2 Boffi (10.1016/j.apples.2021.100038_bib0007) 2013 Bugliarello (10.1016/j.apples.2021.100038_bib0009) 1963; 7 Nubar (10.1016/j.apples.2021.100038_bib0026) 1971; 11 Hron (10.1016/j.apples.2021.100038_bib0016) 2008; 56 Mekhlouf (10.1016/j.apples.2021.100038_bib0020) 2017; 4 Stokes (10.1016/j.apples.2021.100038_bib0033) 2011; 21 Urquiza (10.1016/j.apples.2021.100038_bib0035) 2014; 256 10.1016/j.apples.2021.100038_bib0001 Babuška (10.1016/j.apples.2021.100038_bib0003) 1959; 39 Balay (10.1016/j.apples.2021.100038_bib0004) 2020 Bennett (10.1016/j.apples.2021.100038_bib0006) 1967; 155 Rajagopal (10.1016/j.apples.2021.100038_bib0029) 2020; 8 Dione (10.1016/j.apples.2021.100038_bib0012) 2013; 27 Misra (10.1016/j.apples.2021.100038_bib0021) 2007; 07 Neto (10.1016/j.apples.2021.100038_bib0023) 2005; 68 Nitsche (10.1016/j.apples.2021.100038_bib0024) 1971; 36 Poisson (10.1016/j.apples.2021.100038_bib0027) 1831; 13 de Prony, G.C.F.M.R.B. (10.1016/j.apples.2021.100038_bib0028) 1804 Verfürth (10.1016/j.apples.2021.100038_bib0036) 1986; 50 Juntunen (10.1016/j.apples.2021.100038_bib0017) 2009; 78 Braack (10.1016/j.apples.2021.100038_bib0008) 2014; 32 Womersley (10.1016/j.apples.2021.100038_bib0039) 1955; 127 Rieder (10.1016/j.apples.2021.100038_bib0030) 1974; 1 Madukauwa-David (10.1016/j.apples.2021.100038_bib0019) 2018; 93 Nubar (10.1016/j.apples.2021.100038_bib0025) 1967; 4 Burman (10.1016/j.apples.2021.100038_bib0010) 2012; 50 Navier (10.1016/j.apples.2021.100038_bib0022) 1823; 6 Girard (10.1016/j.apples.2021.100038_bib0015) 1813 Alnæs (10.1016/j.apples.2021.100038_bib0002) 2015; 3 10.1016/j.apples.2021.100038_bib0031 Švihlová (10.1016/j.apples.2021.100038_bib0034) 2017; 114 Verfürth (10.1016/j.apples.2021.100038_bib0037) 1991; 59 Du Buat (10.1016/j.apples.2021.100038_bib0013) 1786 Stokes (10.1016/j.apples.2021.100038_bib0032) 1845; 8 |
| References_xml | – volume: 7 start-page: 209 year: 1963 end-page: 230 ident: bib0009 article-title: Detailed characteristics of the flow of blood in vitro publication-title: Trans. Soc. Rheol. – year: 2013 ident: bib0007 publication-title: Mixed Finite Element Methods and Applications – volume: 8 start-page: 91 year: 2020 end-page: 97 ident: bib0029 article-title: Modeling of the aorta: complexities and inadequacies publication-title: Aorta – year: 2020 ident: bib0004 article-title: PETSc Users Manual publication-title: Technical Report – volume: 11 start-page: 252 year: 1971 end-page: 264 ident: bib0026 article-title: Blood flow, slip, and viscometry publication-title: Biophys. J. – year: 1804 ident: bib0028 article-title: Researches Physico-Mathématiques sur la Théorie des Eaux Courantes. publication-title: Paris. – volume: 32 start-page: 507 year: 2014 end-page: 521 ident: bib0008 article-title: Directional Do-nothing condition for the Navier-Stokes equations publication-title: J. Comput. Math. – volume: 59 start-page: 615 year: 1991 end-page: 636 ident: bib0037 article-title: Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II publication-title: Numerische Mathematik – volume: 2 start-page: 225 year: 1982 end-page: 238 ident: bib0014 article-title: The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow publication-title: Int. J. Numer. Methods Fluids – volume: 13 start-page: 1 year: 1831 end-page: 175 ident: bib0027 article-title: Mémoire sur les équations générales de l’équilibre et du mouvement des corps solides élastiques et des fluides publication-title: Journal de l’École Polytechnique – volume: 07 start-page: 337 year: 2007 end-page: 353 ident: bib0021 article-title: Role of slip velocity in blood flow through stenosed arteries: a non-Newtonian model publication-title: J. Mech. Med. Biol. – volume: 27 start-page: 283 year: 2013 end-page: 296 ident: bib0012 article-title: Stokes equations with penalised slip boundary conditions publication-title: Int. J. Comput. Fluid Dyn. – volume: 4 start-page: 133150 year: 1967 ident: bib0025 article-title: Effect of slip on the rheology of a composite fluid: application to blood publication-title: Biorheology – volume: 155 start-page: 1554 year: 1967 end-page: 1556 ident: bib0006 article-title: Red cell slip at a wall in vitro publication-title: Science – volume: 3 year: 1800 ident: bib0011 article-title: Expériences destinées á déterminer la cohérence des fluides et les lois de leur résistance dans les mouvements trés lents. publication-title: Mémoires de l’Institut National des Sciences et Arts. Sciences Mathématiques et Physiques – volume: 127 start-page: 553 year: 1955 end-page: 563 ident: bib0039 article-title: Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known publication-title: J. Physiol. – volume: 295 start-page: 240 year: 2015 end-page: 267 ident: bib0005 article-title: Finite element formulation of general boundary conditions for incompressible flows publication-title: Comput. Methods Appl. Mech. Eng. – start-page: 249 year: 1813 end-page: 380 ident: bib0015 article-title: Sur le mouvement des fluides dans les tubes capillaires, et l’influence ed la temperature sur ce mouvement. publication-title: Mémoires des Classe des Sciences Matheḿatiques et Physiques d’la Institut des France. – volume: 4 start-page: 54 year: 2017 end-page: 63 ident: bib0020 article-title: Assessment of Nitsche’s Method for Dirichlet boundary conditions treatment publication-title: J. Fluid Flow Heat Mass Transf. – volume: 256 start-page: 748 year: 2014 end-page: 767 ident: bib0035 article-title: Weak imposition of the slip boundary condition on curved boundaries for stokes flow publication-title: J. Comput. Phys. – volume: 78 start-page: 1353 year: 2009 end-page: 1374 ident: bib0017 article-title: Nitsche’s method for general boundary conditions publication-title: Math. Comput. – volume: 36 start-page: 9 year: 1971 end-page: 15 ident: bib0024 article-title: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräiumen, die keinen Randbedingungen unterworfen sind. publication-title: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – volume: 56 start-page: 2128 year: 2008 end-page: 2143 ident: bib0016 article-title: Flows of Incompressible Fluids subject to Navier’s slip on the boundary publication-title: Comput. Math. Appl. – volume: 3 year: 2015 ident: bib0002 article-title: The FEniCS project version 1.5 publication-title: Arch. Numer. Softw. – volume: 39 start-page: 411 year: 1959 end-page: 412 ident: bib0003 article-title: Die Abhängigkeit der Lösung der Elastizitätsprobleme von kleinen Veränderungen des Definitionsgebietes publication-title: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik – start-page: 189 year: 2003 end-page: 196 ident: bib0038 article-title: Taylor-Hood elements in 3D publication-title: Analysis and Simulation of Multifield Problems – volume: 21 start-page: 668 year: 2011 end-page: 702 ident: bib0033 article-title: On generalised penalty approaches for slip, free surface and related boundary conditions in viscous flow simulation publication-title: Int. J. Numer. Methods Heat Fluid Flow – volume: 114 start-page: 1 year: 2017 end-page: 15 ident: bib0034 article-title: Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis publication-title: Int. J. Eng. Sci. – volume: 8 start-page: 287 year: 1845 end-page: 305 ident: bib0032 article-title: On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids publication-title: Trans. Camb. Philos. Soc. – volume: 50 start-page: 697 year: 1986 end-page: 721 ident: bib0036 article-title: Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition publication-title: Numerische Mathematik – volume: 38 start-page: 129 year: 1999 end-page: 142 ident: bib0018 article-title: Weak imposition of “no-slip” conditions in finite element methods publication-title: Comput. Math. Appl. – reference: Abhyankar, S., Brown, J., Constantinescu, E. M., Ghosh, D., Smith, B. F., Zhang, H., 2018. PETSc/TS: A Modern Scalable ODE/DAE Solver Library. – volume: 93 start-page: 134 year: 2018 end-page: 140 ident: bib0019 article-title: Characterization of aortic root geometry in transcatheter aortic valve replacement patients publication-title: Catheter. Cardiovasc. Interven. – volume: 68 start-page: 2859 year: 2005 end-page: 2897 ident: bib0023 article-title: Boundary slip in Newtonian liquids: a review of experimental studies publication-title: Rep. Prog. Phys. – volume: 50 start-page: 1959 year: 2012 end-page: 1981 ident: bib0010 article-title: A penalty-free nonsymmetric Nitsche-type method for the weak imposition of boundary conditions publication-title: SIAM J. Numer. Anal. – year: 1786 ident: bib0013 article-title: Principes d’hydraulique et de pyrodynamique vérifiés par un grand nombre déxpériences faites par ordre du gouvernement publication-title: (ed. princeps en 1 vol. 1779, 2e ed. en 2 vol. 1786, derniére ed. révisée en 3 vol. 1816), ed. Firmin Didot, Paris. – reference: Sime, N., Wilson, C. R., 2020. Automatic weak imposition of free slip boundary conditions via Nitsche’s method: application to nonlinear problems in geodynamics. – volume: 6 start-page: 389 year: 1823 end-page: 416 ident: bib0022 article-title: Mémoire sur les lois du mouvement des fluides publication-title: Mém Acad Sci, Institut de France – volume: 1 start-page: 51 year: 1974 end-page: 53 ident: bib0030 article-title: On the plate paradox of Sapondzhyan and Babuška publication-title: Mech. Res. Commun. – year: 2020 ident: 10.1016/j.apples.2021.100038_bib0004 article-title: PETSc Users Manual – volume: 8 start-page: 287 year: 1845 ident: 10.1016/j.apples.2021.100038_bib0032 article-title: On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids publication-title: Trans. Camb. Philos. Soc. – start-page: 189 year: 2003 ident: 10.1016/j.apples.2021.100038_bib0038 article-title: Taylor-Hood elements in 3D – volume: 78 start-page: 1353 issue: 267 year: 2009 ident: 10.1016/j.apples.2021.100038_bib0017 article-title: Nitsche’s method for general boundary conditions publication-title: Math. Comput. doi: 10.1090/S0025-5718-08-02183-2 – ident: 10.1016/j.apples.2021.100038_bib0001 – volume: 21 start-page: 668 issue: 6 year: 2011 ident: 10.1016/j.apples.2021.100038_bib0033 article-title: On generalised penalty approaches for slip, free surface and related boundary conditions in viscous flow simulation publication-title: Int. J. Numer. Methods Heat Fluid Flow doi: 10.1108/09615531111148455 – volume: 13 start-page: 1 year: 1831 ident: 10.1016/j.apples.2021.100038_bib0027 article-title: Mémoire sur les équations générales de l’équilibre et du mouvement des corps solides élastiques et des fluides publication-title: Journal de l’École Polytechnique – volume: 1 start-page: 51 issue: 1 year: 1974 ident: 10.1016/j.apples.2021.100038_bib0030 article-title: On the plate paradox of Sapondzhyan and Babuška publication-title: Mech. Res. Commun. doi: 10.1016/0093-6413(74)90036-6 – volume: 4 start-page: 54 year: 2017 ident: 10.1016/j.apples.2021.100038_bib0020 article-title: Assessment of Nitsche’s Method for Dirichlet boundary conditions treatment publication-title: J. Fluid Flow Heat Mass Transf. – volume: 07 start-page: 337 issue: 03 year: 2007 ident: 10.1016/j.apples.2021.100038_bib0021 article-title: Role of slip velocity in blood flow through stenosed arteries: a non-Newtonian model publication-title: J. Mech. Med. Biol. doi: 10.1142/S0219519407002303 – volume: 2 start-page: 225 issue: 3 year: 1982 ident: 10.1016/j.apples.2021.100038_bib0014 article-title: The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.1650020302 – ident: 10.1016/j.apples.2021.100038_bib0031 – volume: 59 start-page: 615 issue: 1 year: 1991 ident: 10.1016/j.apples.2021.100038_bib0037 article-title: Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II publication-title: Numerische Mathematik doi: 10.1007/BF01385799 – volume: 32 start-page: 507 issue: 5 year: 2014 ident: 10.1016/j.apples.2021.100038_bib0008 article-title: Directional Do-nothing condition for the Navier-Stokes equations publication-title: J. Comput. Math. doi: 10.4208/jcm.1405-m4347 – start-page: 249 year: 1813 ident: 10.1016/j.apples.2021.100038_bib0015 article-title: Sur le mouvement des fluides dans les tubes capillaires, et l’influence ed la temperature sur ce mouvement. – volume: 11 start-page: 252 issue: 3 year: 1971 ident: 10.1016/j.apples.2021.100038_bib0026 article-title: Blood flow, slip, and viscometry publication-title: Biophys. J. doi: 10.1016/S0006-3495(71)86212-4 – volume: 155 start-page: 1554 issue: 3769 year: 1967 ident: 10.1016/j.apples.2021.100038_bib0006 article-title: Red cell slip at a wall in vitro publication-title: Science doi: 10.1126/science.155.3769.1554 – volume: 36 start-page: 9 year: 1971 ident: 10.1016/j.apples.2021.100038_bib0024 article-title: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräiumen, die keinen Randbedingungen unterworfen sind. publication-title: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg doi: 10.1007/BF02995904 – volume: 3 issue: 100 year: 2015 ident: 10.1016/j.apples.2021.100038_bib0002 article-title: The FEniCS project version 1.5 publication-title: Arch. Numer. Softw. – volume: 93 start-page: 134 issue: 1 year: 2018 ident: 10.1016/j.apples.2021.100038_bib0019 article-title: Characterization of aortic root geometry in transcatheter aortic valve replacement patients publication-title: Catheter. Cardiovasc. Interven. doi: 10.1002/ccd.27805 – volume: 127 start-page: 553 year: 1955 ident: 10.1016/j.apples.2021.100038_bib0039 article-title: Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known publication-title: J. Physiol. doi: 10.1113/jphysiol.1955.sp005276 – volume: 50 start-page: 1959 issue: 4 year: 2012 ident: 10.1016/j.apples.2021.100038_bib0010 article-title: A penalty-free nonsymmetric Nitsche-type method for the weak imposition of boundary conditions publication-title: SIAM J. Numer. Anal. doi: 10.1137/10081784X – volume: 6 start-page: 389 year: 1823 ident: 10.1016/j.apples.2021.100038_bib0022 article-title: Mémoire sur les lois du mouvement des fluides publication-title: Mém Acad Sci, Institut de France – volume: 8 start-page: 91 issue: 4 year: 2020 ident: 10.1016/j.apples.2021.100038_bib0029 article-title: Modeling of the aorta: complexities and inadequacies publication-title: Aorta doi: 10.1055/s-0040-1715588 – volume: 39 start-page: 411 issue: 9-11 year: 1959 ident: 10.1016/j.apples.2021.100038_bib0003 article-title: Die Abhängigkeit der Lösung der Elastizitätsprobleme von kleinen Veränderungen des Definitionsgebietes publication-title: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik doi: 10.1002/zamm.19590390947 – volume: 50 start-page: 697 issue: 6 year: 1986 ident: 10.1016/j.apples.2021.100038_bib0036 article-title: Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition publication-title: Numerische Mathematik doi: 10.1007/BF01398380 – volume: 3 year: 1800 ident: 10.1016/j.apples.2021.100038_bib0011 article-title: Expériences destinées á déterminer la cohérence des fluides et les lois de leur résistance dans les mouvements trés lents. – volume: 56 start-page: 2128 issue: 8 year: 2008 ident: 10.1016/j.apples.2021.100038_bib0016 article-title: Flows of Incompressible Fluids subject to Navier’s slip on the boundary publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2008.03.058 – volume: 68 start-page: 2859 issue: 12 year: 2005 ident: 10.1016/j.apples.2021.100038_bib0023 article-title: Boundary slip in Newtonian liquids: a review of experimental studies publication-title: Rep. Prog. Phys. doi: 10.1088/0034-4885/68/12/R05 – volume: 7 start-page: 209 issue: 1 year: 1963 ident: 10.1016/j.apples.2021.100038_bib0009 article-title: Detailed characteristics of the flow of blood in vitro publication-title: Trans. Soc. Rheol. doi: 10.1122/1.548964 – volume: 295 start-page: 240 year: 2015 ident: 10.1016/j.apples.2021.100038_bib0005 article-title: Finite element formulation of general boundary conditions for incompressible flows publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2015.07.002 – volume: 4 start-page: 133150 issue: 4 year: 1967 ident: 10.1016/j.apples.2021.100038_bib0025 article-title: Effect of slip on the rheology of a composite fluid: application to blood publication-title: Biorheology doi: 10.3233/BIR-1967-4401 – year: 2013 ident: 10.1016/j.apples.2021.100038_bib0007 – volume: 27 start-page: 283 issue: 6-7 year: 2013 ident: 10.1016/j.apples.2021.100038_bib0012 article-title: Stokes equations with penalised slip boundary conditions publication-title: Int. J. Comput. Fluid Dyn. doi: 10.1080/10618562.2013.821114 – year: 1786 ident: 10.1016/j.apples.2021.100038_bib0013 article-title: Principes d’hydraulique et de pyrodynamique vérifiés par un grand nombre déxpériences faites par ordre du gouvernement – volume: 114 start-page: 1 year: 2017 ident: 10.1016/j.apples.2021.100038_bib0034 article-title: Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis publication-title: Int. J. Eng. Sci. doi: 10.1016/j.ijengsci.2017.01.002 – volume: 38 start-page: 129 issue: 5-6 year: 1999 ident: 10.1016/j.apples.2021.100038_bib0018 article-title: Weak imposition of “no-slip” conditions in finite element methods publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(99)00220-5 – year: 1804 ident: 10.1016/j.apples.2021.100038_bib0028 article-title: Researches Physico-Mathématiques sur la Théorie des Eaux Courantes. – volume: 256 start-page: 748 year: 2014 ident: 10.1016/j.apples.2021.100038_bib0035 article-title: Weak imposition of the slip boundary condition on curved boundaries for stokes flow publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2013.08.045 |
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| Title | A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions |
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