Close Search Advanced
Journals
Resources
About Us
Open Access

Directional Do-Nothing Condition for the Navier-Stokes Equations

Directional Do-Nothing Condition for the Navier-Stokes Equations
Preview
Add to basket

Year:    2014

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 5 : pp. 507–521

Abstract

The numerical solution of flow problems usually requires bounded domains although the physical problem may take place in an unbounded or substantially larger domain. In this case, artificial boundaries are necessary. A well established artificial boundary condition for the Navier-Stokes equations discretized by finite elements is the "do-nothing" condition. The reason for this is the fact that this condition appears automatically in the variational formulation after partial integration of the viscous term and the pressure gradient. This condition is one of the most established outflow conditions for Navier-Stokes but there are very few analytical insight into this boundary condition. We address the question of existence and stability of weak solutions for the Navier-Stokes equations with a "directional do-nothing" condition. In contrast to the usual "do-nothing" condition this boundary condition has enhanced stability properties. In the case of pure outflow, the condition is equivalent to the original one, whereas in the case of inflow a dissipative effect appears. We show existence of weak solutions and illustrate the effect of this boundary condition by computation of steady and non-steady flows.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1405-m4347

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 5 : pp. 507–521

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Boundary conditions Navier-Stokes Outflow condition Existence.

  1. Variational resolution of outflow boundary conditions for incompressible Navier–Stokes

    Bathory, Michal | Stefanelli, Ulisse

    Nonlinearity, Vol. 35 (2022), Iss. 11 P.5553

    https://doi.org/10.1088/1361-6544/ac8fd8 [Citations: 0]

  2. On numerical simulation of flow problems in three dimension: energy conservation in fluid-structure interactions

    Sváček, Petr | Dančová, Petra | Vít, Tomáš

    EPJ Web of Conferences, Vol. 92 (2015), Iss. P.02089

    https://doi.org/10.1051/epjconf/20159202089 [Citations: 0]

  3. Nonlinear dynamics of fully developed swirling jets

    Douglas, Christopher M. | Emerson, Benjamin L. | Lieuwen, Timothy C.

    Journal of Fluid Mechanics, Vol. 924 (2021), Iss.

    https://doi.org/10.1017/jfm.2021.615 [Citations: 12]

  4. On a simple and effective thermal open boundary condition for convective heat transfer problems

    Liu, Xiaoyu | Xie, Zhi | Dong, Suchuan

    International Journal of Heat and Mass Transfer, Vol. 151 (2020), Iss. P.119355

    https://doi.org/10.1016/j.ijheatmasstransfer.2020.119355 [Citations: 14]

  5. A convective boundary condition for the Navier–Stokes equations

    Simon, John Sebastian H. | Notsu, Hirofumi

    Applied Mathematics Letters, Vol. 128 (2022), Iss. P.107876

    https://doi.org/10.1016/j.aml.2021.107876 [Citations: 5]

  6. Energy-stable boundary conditions based on a quadratic form: Applications to outflow/open-boundary problems in incompressible flows

    Ni, Naxian | Yang, Zhiguo | Dong, Suchuan

    Journal of Computational Physics, Vol. 391 (2019), Iss. P.179

    https://doi.org/10.1016/j.jcp.2019.04.030 [Citations: 9]
  7. Fluid-structure Interactions

    Models

    Richter, Thomas

    2017

    https://doi.org/10.1007/978-3-319-63970-3_2 [Citations: 0]

  8. Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

    Terekhov, Kirill M. | Butakov, Ivan D. | Danilov, Alexander A. | Vassilevski, Yuri V.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 39 (2023), Iss. 11

    https://doi.org/10.1002/cnm.3731 [Citations: 2]

  9. Benchmark problems for numerical treatment of backflow at open boundaries

    Bertoglio, Cristóbal | Caiazzo, Alfonso | Bazilevs, Yuri | Braack, Malte | Esmaily, Mahdi | Gravemeier, Volker | L. Marsden, Alison | Pironneau, Olivier | E. Vignon‐Clementel, Irene | A. Wall, Wolfgang

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 34 (2018), Iss. 2

    https://doi.org/10.1002/cnm.2918 [Citations: 45]
  10. Nonlinear Differential Equations and Applications

    Navier–Stokes Equations with Regularized Directional Boundary Condition

    Nogueira, Pedro | Silvestre, Ana L.

    2024

    https://doi.org/10.1007/978-3-031-53740-0_11 [Citations: 0]

  11. MHD natural convective flow of Fe3O4−H2O ferrofluids in an inclined partial open complex-wavy-walls ringed enclosures using non-linear Boussinesq approximation

    Elshehabey, Hillal M. | Raizah, Zehba | Öztop, Hakan F. | Ahmed, Sameh E.

    International Journal of Mechanical Sciences, Vol. 170 (2020), Iss. P.105352

    https://doi.org/10.1016/j.ijmecsci.2019.105352 [Citations: 57]

  12. Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

    Valášek, J. | Sváček, P. | Horáček, J. | Dančová, P. | Veselý, M.

    EPJ Web of Conferences, Vol. 114 (2016), Iss. P.02130

    https://doi.org/10.1051/epjconf/201611402130 [Citations: 1]

  13. Solvability in a finite pipe of steady-state Navier–Stokes equations with boundary conditions involving Bernoulli pressure

    Korobkov, Mikhail V. | Pileckas, Konstantin | Russo, Remigio

    Calculus of Variations and Partial Differential Equations, Vol. 59 (2020), Iss. 1

    https://doi.org/10.1007/s00526-019-1688-8 [Citations: 7]

  14. The Boussinesq system with mixed non-smooth boundary conditions and do-nothing boundary flow

    Ceretani, Andrea N. | Rautenberg, Carlos N.

    Zeitschrift für angewandte Mathematik und Physik, Vol. 70 (2019), Iss. 1

    https://doi.org/10.1007/s00033-018-1058-y [Citations: 12]

  15. On the steady motion of Navier–Stokes flows past a fixed obstacle in a three-dimensional channel under mixed boundary conditions

    Sperone, Gianmarco

    Annali di Matematica Pura ed Applicata (1923 -), Vol. 200 (2021), Iss. 5 P.1961

    https://doi.org/10.1007/s10231-021-01066-w [Citations: 4]

  16. Impact of viscosity modeling on the simulation of aortic blood flow

    Katz, Sarah | Caiazzo, Alfonso | John, Volker

    Journal of Computational and Applied Mathematics, Vol. 425 (2023), Iss. P.115036

    https://doi.org/10.1016/j.cam.2022.115036 [Citations: 2]

  17. A Stokes-residual backflow stabilization method applied to physiological flows

    Bertoglio, Cristóbal | Caiazzo, Alfonso

    Journal of Computational Physics, Vol. 313 (2016), Iss. P.260

    https://doi.org/10.1016/j.jcp.2016.02.045 [Citations: 17]

  18. On the incorporation of obstacles in a fluid flow problem using a Navier–Stokes–Brinkman penalization approach

    Fuchsberger, Jana | Aigner, Philipp | Niederer, Steven | Plank, Gernot | Schima, Heinrich | Haase, Gundolf | Karabelas, Elias

    Journal of Computational Science, Vol. 57 (2022), Iss. P.101506

    https://doi.org/10.1016/j.jocs.2021.101506 [Citations: 12]

  19. The spatial operator in the incompressible Navier–Stokes, Oseen and Stokes equations

    Nordström, Jan | Laurén, Fredrik

    Computer Methods in Applied Mechanics and Engineering, Vol. 363 (2020), Iss. P.112857

    https://doi.org/10.1016/j.cma.2020.112857 [Citations: 9]

  20. Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load

    Karabelas, Elias | Gsell, Matthias A. F. | Augustin, Christoph M. | Marx, Laura | Neic, Aurel | Prassl, Anton J. | Goubergrits, Leonid | Kuehne, Titus | Plank, Gernot

    Frontiers in Physiology, Vol. 9 (2018), Iss.

    https://doi.org/10.3389/fphys.2018.00538 [Citations: 26]

  21. Distributed parameter identification for the Navier–Stokes equations for obstacle detection

    Aguayo, Jorge | Bertoglio, Cristóbal | Osses, Axel

    Inverse Problems, Vol. 40 (2024), Iss. 1 P.015012

    https://doi.org/10.1088/1361-6420/ad1133 [Citations: 0]

  22. A distributed resistance inverse method for flow obstacle identification from internal velocity measurements

    Aguayo, Jorge | Bertoglio, Cristóbal | Osses, Axel

    Inverse Problems, Vol. 37 (2021), Iss. 2 P.025010

    https://doi.org/10.1088/1361-6420/abced8 [Citations: 5]

  23. Implicit-explicit Schemes for Incompressible Flow Problems with Variable Viscosity

    Barrenechea, Gabriel | Castillo, Ernesto | Pacheco, Douglas

    SIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 4 P.A2660

    https://doi.org/10.1137/23M1606526 [Citations: 0]

  24. On aerodynamic force computation in fluid–structure interaction problems — Comparison of different approaches

    Valášek, Jan | Sváček, Petr

    Journal of Computational and Applied Mathematics, Vol. 429 (2023), Iss. P.115208

    https://doi.org/10.1016/j.cam.2023.115208 [Citations: 3]

  25. A posteriori error estimation for the steady Navier–Stokes equations in random domains

    Guignard, Diane | Nobile, Fabio | Picasso, Marco

    Computer Methods in Applied Mechanics and Engineering, Vol. 313 (2017), Iss. P.483

    https://doi.org/10.1016/j.cma.2016.10.008 [Citations: 9]
  26. Multiscale Analysis of Viscous Flows in Thin Tube Structures

    Steady-State Stokes and Navier–Stokes Equations in Tube Structures

    Panasenko, Grigory | Pileckas, Konstantin

    2024

    https://doi.org/10.1007/978-3-031-54630-3_5 [Citations: 0]

  27. Finite Element Analysis of Laminar Heat Transfer within an Axial-Flux Permanent Magnet Machine

    Willems, Robin | Friedrich, Léo A. J. | Verhoosel, Clemens V.

    Mathematical and Computational Applications, Vol. 26 (2021), Iss. 1 P.23

    https://doi.org/10.3390/mca26010023 [Citations: 1]
  28. Proceedings of the 14th International Conference on Vibration Problems

    The Flow-Induced Vibrations of Vocal Folds Approximated by the Finite Element Method

    Valášek, Jan | Sváček, Petr | Horáček, Jaromír

    2021

    https://doi.org/10.1007/978-981-15-8049-9_23 [Citations: 0]

  29. Aeroacoustic computation of fluid-structure interaction problems with low Mach numbers

    Valášek, Jan | Sváček, Petr | Dančová, P.

    EPJ Web of Conferences, Vol. 180 (2018), Iss. P.02113

    https://doi.org/10.1051/epjconf/201818002113 [Citations: 0]

  30. LU factorizations and ILU preconditioning for stabilized discretizations of incompressible Navier–Stokes equations

    Konshin, Igor | Olshanskii, Maxim | Vassilevski, Yuri

    Numerical Linear Algebra with Applications, Vol. 24 (2017), Iss. 3

    https://doi.org/10.1002/nla.2085 [Citations: 6]

  31. On existence and uniqueness of solutions to a Boussinesq system with nonlinear and mixed boundary conditions

    Arndt, Rafael | Ceretani, Andrea N. | Rautenberg, Carlos N.

    Journal of Mathematical Analysis and Applications, Vol. 490 (2020), Iss. 1 P.124201

    https://doi.org/10.1016/j.jmaa.2020.124201 [Citations: 5]
  32. Finite Element Methods for Incompressible Flow Problems

    The Navier–Stokes Equations as Model for Incompressible Flows

    John, Volker

    2016

    https://doi.org/10.1007/978-3-319-45750-5_2 [Citations: 0]

  33. On numerical simulation of fluid - structure interaction problems using variational multiscale methods

    Sváček, Petr

    Journal of Computational and Applied Mathematics, Vol. 427 (2023), Iss. P.115125

    https://doi.org/10.1016/j.cam.2023.115125 [Citations: 1]

  34. A Note on Global Attractors for a Transition to Turbulence ODE Model Problem

    Singler, John R.

    Differential Equations and Dynamical Systems, Vol. 32 (2024), Iss. 3 P.709

    https://doi.org/10.1007/s12591-022-00590-2 [Citations: 0]

  35. Spectral properties of the incompressible Navier-Stokes equations

    Laurén, Fredrik | Nordström, Jan

    Journal of Computational Physics, Vol. 429 (2021), Iss. P.110019

    https://doi.org/10.1016/j.jcp.2020.110019 [Citations: 2]

  36. Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

    John, Volker | Knobloch, Petr | Novo, Julia

    Computing and Visualization in Science, Vol. 19 (2018), Iss. 5-6 P.47

    https://doi.org/10.1007/s00791-018-0290-5 [Citations: 55]

  37. A divergence‐conforming hybridized discontinuous Galerkin method for the incompressible Reynolds‐averaged Navier‐Stokes equations

    Peters, Eric L. | Evans, John A.

    International Journal for Numerical Methods in Fluids, Vol. 91 (2019), Iss. 3 P.112

    https://doi.org/10.1002/fld.4745 [Citations: 7]
  38. Fluids Under Control

    Numerical Simulation of Fluid-Structure-Acoustic Interactions Models of Human Phonation Process

    Sváček, Petr | Valášek, Jan

    2023

    https://doi.org/10.1007/978-3-031-27625-5_11 [Citations: 0]

  39. Preconditioning immersed isogeometric finite element methods with application to flow problems

    de Prenter, F. | Verhoosel, C.V. | van Brummelen, E.H.

    Computer Methods in Applied Mechanics and Engineering, Vol. 348 (2019), Iss. P.604

    https://doi.org/10.1016/j.cma.2019.01.030 [Citations: 39]

  40. A validated patient-specific FSI model for vascular access in haemodialysis

    de Villiers, A. M. | McBride, A. T. | Reddy, B. D. | Franz, T. | Spottiswoode, B. S.

    Biomechanics and Modeling in Mechanobiology, Vol. 17 (2018), Iss. 2 P.479

    https://doi.org/10.1007/s10237-017-0973-8 [Citations: 20]

  41. On the performance of the DG method with a directional do-nothing boundary condition

    Garcia, Aureo Quintas | Gomes, Francisco Augusto Aparecido | Hecke, Mildred Ballin

    Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 39 (2017), Iss. 10 P.3919

    https://doi.org/10.1007/s40430-017-0868-8 [Citations: 1]
  42. Finite Element Methods for Incompressible Flow Problems

    The Steady-State Navier–Stokes Equations

    John, Volker

    2016

    https://doi.org/10.1007/978-3-319-45750-5_6 [Citations: 0]

  43. Numerical considerations for advection‐diffusion problems in cardiovascular hemodynamics

    Lynch, Sabrina R. | Nama, Nitesh | Xu, Zelu | Arthurs, Christopher J. | Sahni, Onkar | Figueroa, C. Alberto

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 36 (2020), Iss. 9

    https://doi.org/10.1002/cnm.3378 [Citations: 6]

  44. Analysis and assessment of a monolithic FSI finite element method

    Lozovskiy, Alexander | Olshanskii, Maxim A. | Vassilevski, Yuri V.

    Computers & Fluids, Vol. 179 (2019), Iss. P.277

    https://doi.org/10.1016/j.compfluid.2018.11.004 [Citations: 21]

  45. Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: A study of aortic valve stenosis

    Švihlová, H. | Hron, J. | Málek, J. | Rajagopal, K.R. | Rajagopal, K.

    International Journal of Engineering Science, Vol. 113 (2017), Iss. P.37

    https://doi.org/10.1016/j.ijengsci.2017.01.001 [Citations: 1]

  46. On existence, regularity and uniqueness of thermally coupled incompressible flows in a system of three dimensional pipes

    Beneš, Michal | Pažanin, Igor

    Nonlinear Analysis: Theory, Methods & Applications, Vol. 149 (2017), Iss. P.56

    https://doi.org/10.1016/j.na.2016.10.007 [Citations: 10]

  47. Numerical simulation of fluid-structure interactions with stabilized finite element method

    Sváček, Petr

    Advances in Engineering Software, Vol. 113 (2017), Iss. P.96

    https://doi.org/10.1016/j.advengsoft.2016.08.012 [Citations: 2]

  48. Pressure-correction projection method for modelling the incompressible fluid flow in porous media

    Terekhov, Kirill M.

    Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 38 (2023), Iss. 4 P.241

    https://doi.org/10.1515/rnam-2023-0019 [Citations: 0]
  49. Personalized Computational Hemodynamics

    Bibliography

    2020

    https://doi.org/10.1016/B978-0-12-815653-7.16001-4 [Citations: 0]
  50. Numerical Mathematics and Advanced Applications ENUMATH 2019

    Numerical Approximation of Fluid-Structure Interaction Problem in a Closing Channel Near the Stability Boundary

    Valášek, Jan | Sváček, Petr | Horáček, Jaromír

    2021

    https://doi.org/10.1007/978-3-030-55874-1_107 [Citations: 0]

  51. Grad-div stabilized discretizations on S-type meshes for the Oseen problem

    Franz, Sebastian | Höhne, Katharina | Matthies, Gunar

    IMA Journal of Numerical Analysis, Vol. 38 (2018), Iss. 1 P.299

    https://doi.org/10.1093/imanum/drw069 [Citations: 3]

  52. A Variational Multiscale Method for Particle Dispersion Modeling in the Atmosphere

    Nishio, Y. | Janssens, B. | Limam, K. | van Beeck, J.

    Fluid Dynamics & Materials Processing, Vol. 19 (2023), Iss. 3 P.743

    https://doi.org/10.32604/fdmp.2022.021848 [Citations: 0]

  53. Aeroacoustic computation of fluid-structure interaction problems with low Mach numbers

    Valášek, Jan | Sváček, Petr | Dančová, P.

    EPJ Web of Conferences, Vol. 180 (2018), Iss. P.02113

    https://doi.org/10.1051/epjconf/201818002113 [Citations: 0]

  54. On Multiple Solutions to the Steady Flow of Incompressible Fluids Subject to Do-nothing or Constant Traction Boundary Conditions on Artificial Boundaries

    Lanzendörfer, M. | Hron, J.

    Journal of Mathematical Fluid Mechanics, Vol. 22 (2020), Iss. 1

    https://doi.org/10.1007/s00021-019-0472-z [Citations: 4]

  55. Analysis of an electroless plating problem

    Girault, Vivette | Pironneau, Olivier | Wu, Po-Yi

    IMA Journal of Numerical Analysis, Vol. 42 (2022), Iss. 4 P.2884

    https://doi.org/10.1093/imanum/drab075 [Citations: 1]

  56. Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

    Karabelas, Elias | Longobardi, Stefano | Fuchsberger, Jana | Razeghi, Orod | Rodero, Cristobal | Strocchi, Marina | Rajani, Ronak | Haase, Gundolf | Plank, Gernot | Niederer, Steven

    IEEE Transactions on Biomedical Engineering, Vol. 69 (2022), Iss. 10 P.3216

    https://doi.org/10.1109/TBME.2022.3163428 [Citations: 19]

  57. Drag computation for incompressible flows with a Nitsche’s type stabilization method

    Capatina, Daniela | Luce, Robert | Trujillo, David

    Computer Methods in Applied Mechanics and Engineering, Vol. 360 (2020), Iss. P.112775

    https://doi.org/10.1016/j.cma.2019.112775 [Citations: 0]

  58. Thixoviscoplastic flow simulations based on Houska thixotropic and Bingham viscoplastic models

    Begum, Naheed | Ouazzi, Abderrahim | Turek, Stefan

    PAMM, Vol. 24 (2024), Iss. 2

    https://doi.org/10.1002/pamm.202400003 [Citations: 0]

  59. Source Identification of a Chemical Incident in an Urban Area

    Fernández, Francisco J. | Vázquez-Méndez, Miguel E.

    Axioms, Vol. 10 (2021), Iss. 3 P.177

    https://doi.org/10.3390/axioms10030177 [Citations: 0]

  60. A shape design problem for the Navier–Stokes flow with a convective boundary condition

    Simon, J. S. H | Notsu, Hirofumi

    Computational and Applied Mathematics, Vol. 41 (2022), Iss. 4

    https://doi.org/10.1007/s40314-022-01876-5 [Citations: 0]
  61. Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014

    Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows

    Lube, Gert | Arndt, Daniel | Dallmann, Helene

    2015

    https://doi.org/10.1007/978-3-319-25727-3_12 [Citations: 2]

  62. Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis

    Švihlová, H. | Hron, J. | Málek, J. | Rajagopal, K.R. | Rajagopal, K.

    International Journal of Engineering Science, Vol. 114 (2017), Iss. P.1

    https://doi.org/10.1016/j.ijengsci.2017.01.002 [Citations: 12]
  63. Numerical Mathematics and Advanced Applications ENUMATH 2015

    Finite Elements for the Navier-Stokes Problem with Outflow Condition

    Arndt, Daniel | Braack, Malte | Lube, Gert

    2016

    https://doi.org/10.1007/978-3-319-39929-4_10 [Citations: 6]

  64. Numerical simulation of aeroelastic response of an airfoil in flow with laminar–turbulence transition

    Sváček, Petr | Horáček, Jaromír

    Applied Mathematics and Computation, Vol. 267 (2015), Iss. P.28

    https://doi.org/10.1016/j.amc.2015.06.107 [Citations: 2]

  65. Modeling of the unsteady flow through a channel with an artificial outflow condition by the Navier–Stokes variational inequality

    Kračmar, Stanislav | Neustupa, Jiří

    Mathematische Nachrichten, Vol. 291 (2018), Iss. 11-12 P.1801

    https://doi.org/10.1002/mana.201700228 [Citations: 17]
  66. Numerical Mathematics and Advanced Applications ENUMATH 2015

    Numerical Approximation of Interaction of Fluid Flow and Elastic Structure Vibrations

    Valášek, Jan | Sváček, Petr | Horáček, Jaromír

    2016

    https://doi.org/10.1007/978-3-319-39929-4_56 [Citations: 0]
  67. Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014

    Outflow Conditions for the Navier-Stokes Equations with Skew-Symmetric Formulation of the Convective Term

    Braack, Malte

    2015

    https://doi.org/10.1007/978-3-319-25727-3_4 [Citations: 1]

  68. On buoyancy‐driven viscous incompressible flows with various types of boundary conditions

    Beneš, Michal | Kučera, Petr | Vacková, Petra

    ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 103 (2023), Iss. 11

    https://doi.org/10.1002/zamm.202200529 [Citations: 0]

  69. A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions

    Chabiniok, R. | Hron, J. | Jarolímová, A. | Málek, J. | Rajagopal, K.R. | Rajagopal, K. | Švihlová, H. | Tůma, K.

    Applications in Engineering Science, Vol. 6 (2021), Iss. P.100038

    https://doi.org/10.1016/j.apples.2021.100038 [Citations: 3]

  70. Nonreflecting outlet boundary conditions for incompressible flows using SPH

    Alvarado-Rodríguez, Carlos E. | Klapp, Jaime | Sigalotti, Leonardo Di G. | Domínguez, José M. | Cruz Sánchez, Eduardo de la

    Computers & Fluids, Vol. 159 (2017), Iss. P.177

    https://doi.org/10.1016/j.compfluid.2017.09.020 [Citations: 20]
  71. Applications of Differential-Algebraic Equations: Examples and Benchmarks

    Continuous, Semi-discrete, and Fully Discretised Navier-Stokes Equations

    Altmann, R. | Heiland, J.

    2018

    https://doi.org/10.1007/11221_2018_2 [Citations: 3]

  72. On study of the influence of the strength of nonlinear part of boundary condition on the outlet

    Neustupa, T. | Winter, O.

    INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020, (2022), P.020005

    https://doi.org/10.1063/5.0081486 [Citations: 0]

  73. ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier--Stokes Equations

    Konshin, Igor N. | Olshanskii, Maxim A. | Vassilevski, Yuri V.

    SIAM Journal on Scientific Computing, Vol. 37 (2015), Iss. 5 P.A2171

    https://doi.org/10.1137/15M1012311 [Citations: 19]

  74. Artificial boundary conditions for linearized stationary incompressible viscous flow around rotating and translating body

    Deuring, P. | Kračmar, S. | Nečasová, Š.

    Mathematische Nachrichten, Vol. 294 (2021), Iss. 1 P.56

    https://doi.org/10.1002/mana.201900039 [Citations: 1]

  75. Solution of Fluid Dynamics Problems in Truncated Computational Domains

    Potapov, I. I. | Snigur, K. S.

    Computational Mathematics and Mathematical Physics, Vol. 59 (2019), Iss. 3 P.484

    https://doi.org/10.1134/S0965542519030138 [Citations: 0]
  76. Progress in Industrial Mathematics at ECMI 2016

    Numerical Simulation of Flow Induced Vocal Folds Vibration by Stabilized Finite Element Method

    Valášek, Jan | Sváček, Petr | Horáček, Jaromír

    2017

    https://doi.org/10.1007/978-3-319-63082-3_111 [Citations: 0]

  77. Global attractor for a low order ODE model problem for transition to turbulence

    Singler, John R.

    Mathematical Methods in the Applied Sciences, Vol. 40 (2017), Iss. 8 P.2896

    https://doi.org/10.1002/mma.4205 [Citations: 3]

  78. On the Application of Acoustic Analogies in the Numerical Simulation of Human Phonation Process

    Valášek, J. | Kaltenbacher, M. | Sváček, P.

    Flow, Turbulence and Combustion, Vol. 102 (2019), Iss. 1 P.129

    https://doi.org/10.1007/s10494-018-9900-z [Citations: 21]

  79. Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations

    Švihlová, H. | Hron, J. | Málek, J. | Rajagopal, K.R. | Rajagopal, K.

    International Journal of Engineering Science, Vol. 105 (2016), Iss. P.108

    https://doi.org/10.1016/j.ijengsci.2015.11.002 [Citations: 34]

  80. A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem

    Lozovskiy, Alexander | Olshanskii, Maxim A. | Vassilevski, Yuri V.

    Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 37 (2022), Iss. 3 P.159

    https://doi.org/10.1515/rnam-2022-0014 [Citations: 3]

  81. Aeroacoustic simulation of human phonation based on the flow-induced vocal fold vibrations including their contact

    Valášek, Jan | Sváček, Petr

    Advances in Engineering Software, Vol. 194 (2024), Iss. P.103652

    https://doi.org/10.1016/j.advengsoft.2024.103652 [Citations: 0]