A stable pressure-correction MAC scheme for the fluid-Poroelastic material interaction problem

References

• I. Ambartsumyan, E. Khattatov, I. Yotov, and P. Zunino, A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model, Numer. Math. 140(2) (2018), pp. 513–553.
   Web of Science ®Google Scholar
• I. Ambartsumyan, V.J. Ervin, T. Nguyen, and I. Yotov, A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media, ESAIM: Math. Model. Numer. Anal. 53(6) (2019), pp. 1915–1955.
   Google Scholar
• N. Atalla, R. Panneton, and P. Debergue, A mixed displacement-pressure formulation for poroelastic materials, J. Acoust. Soc. Am. 104(1998), pp. 1444–1452.
   Web of Science ®Google Scholar
• S. Badia, A. Quaini, and A. Quarteroni, Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction, J. Comput. Phys. 228(21) (2009), pp. 7986–8014.
   Web of Science ®Google Scholar
• G. Beavers and D. Joseph, Boundary conditions at a naturally impermeable wall, J. Fluid Mech. 30(1967), pp. 197–207.
   Web of Science ®Google Scholar
• W. Boon, M. Hornkjol, M. Kuchta, K.-A. Mardal, and R. Ruiz-Baier, Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers, J. Comput. Phys. 467(2022), pp. 111464. DOI:10.1016/j.jcp.2022.111464.
   Web of Science ®Google Scholar
• M. Bukač, I. Yotov, and P. Zunino, An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure, Numer. Methods Partial Differ. Equ. 31(4) (2015), pp. 1054–1100.
   Web of Science ®Google Scholar
• M. Bukač, I. Yotov, R. Zakerzadeh, and P. Zunino, Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach, Comput. Methods Appl. Mech. Eng. 292(2015), pp. 138–170.
   Web of Science ®Google Scholar
• M. Bukač, A loosely-coupled scheme for the interaction between a fluid, elastic structure and poroelastic material, J. Comput. Phys. 313(2016), pp. 377–399.
   Web of Science ®Google Scholar
• A. Cesmelioglu, Analysis of the coupled Navier-Stokes/Biot problem, J. Math. Anal. Appl. 456(2) (2017), pp. 970–991.
   Web of Science ®Google Scholar
• A. Cesmelioglu and P. Chidyagwai, Numerical analysis of the coupling of free fluid with a poroelastic material, Numer. Methods Partial Differ. Equ. 36(3) (2020), pp. 463–494.
   Web of Science ®Google Scholar
• J. Chen, Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. Part II: three-dimensional solution, Int. J. Solids Struct. 31(2) (1994), pp. 169–202.
   Web of Science ®Google Scholar
• A. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp. 22(1968), pp. 745–762.
   Web of Science ®Google Scholar
• J. Guermond, P. Minev, and J. Shen, Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions, SIAM J. Numer. Anal. 43(1) (2005), pp. 239–258.
   Web of Science ®Google Scholar
• J. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Eng. 195(2006), pp. 6011–6045.
   Web of Science ®Google Scholar
• J. Guermond and J. Shen, Velocity-correction projection methods for incompressible flows, SIAM J. Numer. Anal. 41(1) (2003), pp. 112–134.
   Web of Science ®Google Scholar
• J. Guermond and J. Shen, On the error estimates for the rotational pressure-correction projection methods, Math. Comp. 73(248) (2004), pp. 1719–1737.
   Web of Science ®Google Scholar
• L. Guo and W. Chen, Decoupled modified characteristic finite element method for the time-dependent Navier-Stokes/Biot problem, Numer. Methods Partial Differ. Equ. 38(6) (2022), pp. 1684–1712.
   Web of Science ®Google Scholar
• H. Han and X. Wu, A new mixed finite element formulation and the MAC method for the stokes equations, SIAM J. Numer. Anal. 35(1998), pp. 560–571.
   Web of Science ®Google Scholar
• Y. He and J. Shen, Unconditionally stable pressure-correction schemes for a linear fluid-structure interaction problem, Numer. Math. Theor. Mech. Appl. 7(4) (2014), pp. 537–554.
   Web of Science ®Google Scholar
• Y. He and J. Shen, Unconditionally stable pressure-correction schemes for a nonlinear fluid-structure interaction model, Commun. Appl. Math. Comput. 1(2019), pp. 61–80.
   Google Scholar
• N. Koshiba, J. Ando, M. Chen, and T. Hisada, Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model, J. Biomech. Eng. 129(3) (2007), pp. 374–385.
   PubMed Web of Science ®Google Scholar
• H. Kunwar, H. Lee, and K. Seelman, Second-order time discretization for a coupled quasi-newtonian fluid-poroelastic system, Int. J. Numer. Methods Fluids. 92(7) (2020), pp. 687–702.
   Web of Science ®Google Scholar
• J. Li, M. Yao, M. Mahbub, and H. Zheng, The efficient rotational pressure-correction schemes for the coupling stokes/Darcy problem, Comput. Math. Appl. 79(2020), pp. 337–353.
   Web of Science ®Google Scholar
• A. Lozovskiy, M. Olshanskii, and Y. Vassilevski, A finite element scheme for the numerical solution of the Navier-Stokes/Biot coupled problem, Russian J. Numer. Anal. Math. Model. 37(3) (2022), pp. 159–174.
   Web of Science ®Google Scholar
• M. Murad, J. Guerreiro, and A. Loula, Micromechanical computational modeling of reservoir compaction and surface subsidence, Math. Contemp. 19(2000), pp. 41–69.
   Google Scholar
• O. Oyekole and M. Bukac, Second-order, loosely coupled methods for fluid-poroelastic material interaction, Numer. Methods Partial Differ. Equ. 36(4) (2020), pp. 800–822.
   Web of Science ®Google Scholar
• J. Perot, Conservation properties of unstructured staggered mesh schemes, J. Comput. Phys. 159(1) (2000), pp. 58–89.
   Web of Science ®Google Scholar
• J. Perot, Discrete conservation properties of unstructured mesh schemes, Annu. Rev. Fluid Mech. 43(2011), pp. 299–318.
   Web of Science ®Google Scholar
• R. Ruiz-Baier, M. Taffetani, H. Westermeyer, and I. Yotov, The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye, Comput. Methods Appl. Mech. Eng. 389(2022), Article ID 114384. DOI:10.1016/j.cma.2021.114384.
   Web of Science ®Google Scholar
• J. Shen, On error estimates of projection methods for Navier-Stokes equations: first-order schemes, SIAM J. Numer. Anal. 29(1) (1992), pp. 57–77.
   Web of Science ®Google Scholar
• J. Shen, On error estimates of projection methods for Navier-Stokes equations: second-order schemes, Math. Comput. 65(215) (1996), pp. 1039–1065.
   Web of Science ®Google Scholar
• R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (i), Arch. Rational Mech. Anal. 32(1969), pp. 135–153.
   Web of Science ®Google Scholar
• L. Timmermans, P. Minev, and F. VanDeVosse, An approximate projection scheme for incompressible flow using spectral elements, Internat. J. Numer. Methods Fluids. 22(7) (1996), pp. 673–688.
   Web of Science ®Google Scholar
• B. Tully and Y. Ventikos, Coupling poroelasticity and CFD for cerebrospinal fluid hydrodynamics, IEEE Trans. Biomed. Eng. 56(6) (2009), pp. 1644–1651.
   PubMed Web of Science ®Google Scholar
• H. Wang, Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press, Princeton, NJ, 2004.
   Google Scholar
• X. Wang and H. Rui, The locking-free finite difference method based on staggered grids for the coupled Stokes-Biot problem, Int. J. Comput. Math. 99(10) (2022), pp. 2042–2068.
   Web of Science ®Google Scholar
• J. Wen and Y. He, A strongly conservative finite element method for the coupled Stokes-Biot model, Comput. Math. Appl. 80(5) (2020), pp. 1421–1442.
   Web of Science ®Google Scholar
• R. Zakerzadeh, M. Bukac, and P. Zunino, Computational analysis of energy distribution of coupled blood flow and arterial defomation, Int. J. Adv. Eng. Sci. Appl. Math. 8(2016), pp. 70–85.
   Web of Science ®Google Scholar