An efficient matrix factorization within the projection framework for ameliorating the surface tension time step constraint in interfacial flows
References
[1]
N. Nangia, B.E. Griffith, N.A. Patankar, A.P.S. Bhalla, A robust incompressible Navier-Stokes solver for high density ratio multiphase flows, J. Comput. Phys. 390 (2019) 548–594.
[2]
Z. Yang, M. Lu, S. Wang, A robust solver for incompressible high-Reynolds-number two-fluid flows with high density contrast, J. Comput. Phys. 441 (2021).
[3]
J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100 (1992) 335–354.
[4]
F. Denner, B.G.M. van Wachem, Numerical time-step restrictions as a result of capillary waves, J. Comput. Phys. 285 (2015) 24–40.
[5]
C. Galusinski, P. Vigneaux, On stability condition for bifluid flows with surface tension: application to microfluidics, J. Comput. Phys. 227 (2008) 6140–6164.
[6]
S. Popinet, Numerical models of surface tension, Annu. Rev. Fluid Mech. 50 (2018) 49–75.
[7]
S. Hysing, A new implicit surface tension implementation for interfacial flows, Int. J. Numer. Methods Fluids 51 (2006) 659–672.
[8]
M. Raessi, M. Bussmann, J. Mostaghimi, A semi-implicit finite volume implementation of the csf method for treating surface tension in interfacial flows, Int. J. Numer. Methods Fluids 59 (2009) 1093–1110.
[9]
M. Sussman, M. Ohta, A stable and efficient method for treating surface tension in incompressible two-phase flow, SIAM J. Sci. Comput. 31 (2009) 2447–2471.
[10]
T.Y. Hou, J.S. Lowengrub, M.J. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys. 114 (1994) 312–338.
[11]
J. Hochstein, T. Williams, An implicit surface tension model, in: 34th Aerospace Sciences Meeting and Exhibit, 1996, p. 599.
[12]
A. Jarauta, P. Ryzhakov, J. Pons-Prats, M. Secanell, An implicit surface tension model for the analysis of droplet dynamics, J. Comput. Phys. 374 (2018) 1196–1218.
[13]
E.N. Mahrous, R.V. Roy, A. Jarauta, M. Secanell, A three-dimensional numerical model for the motion of liquid drops by the particle finite element method, Phys. Fluids (2022).
[14]
E. Bänsch, S. Weller, Fully implicit time discretization for a free surface flow problem, PAMM 11 (2011) 619–620.
[15]
F. Denner, F. Evrard, B. van Wachem, Breaching the capillary time-step constraint using a coupled vof method with implicit surface tension, J. Comput. Phys. 459 (2022).
[16]
Z. Yang, S. Dong, An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices, J. Comput. Phys. 393 (2019) 229–257.
[17]
B. Lee, G. Yoon, C. Min, A semi-implicit and unconditionally stable approximation of the surface tension in two-phase fluids, J. Comput. Phys. 397 (2019).
[18]
F. Denner, F. Evrard, R. Serfaty, B.G.M. van Wachem, Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension, Comput. Fluids 143 (2017) 59–72.
[19]
B.E. Griffith, An accurate and efficient method for the incompressible Navier–Stokes equations using the projection method as a preconditioner, J. Comput. Phys. 228 (2009) 7565–7595.
[20]
K. Kim, S.-J. Baek, H.J. Sung, An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations, Int. J. Numer. Methods Fluids 38 (2002) 125–138.
[21]
X. Pan, S. Chun, J.-I. Choi, Efficient monolithic projection-based method for Chemotaxis-driven bioconvection problems, Comput. Math. Appl. 84 (2021) 166–184.
[22]
X. Pan, K.-H. Kim, J.-I. Choi, Efficient monolithic projection method with staggered time discretization for natural convection problems, Int. J. Heat Mass Transf. 144 (2019).
[23]
X. Pan, K. Kim, C. Lee, J.-I. Choi, A decoupled monolithic projection method for natural convection problems, J. Comput. Phys. 314 (2016) 160–166.
[24]
X. Pan, K. Kim, C. Lee, J.-I. Choi, Fully decoupled monolithic projection method for natural convection problems, J. Comput. Phys. 334 (2017) 582–606.
[25]
X. Pan, C. Lee, K. Kim, J.-I. Choi, Analysis of velocity-components decoupled projection method for the incompressible Navier–Stokes equations, Comput. Math. Appl. 71 (2016) 1722–1743.
[26]
U. Lacis, K. Taira, S. Bagheri, A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method, J. Comput. Phys. 305 (2016) 300–318.
[27]
R.-Y. Li, C.-M. Xie, W.-X. Huang, C.-X. Xu, An efficient immersed boundary projection method for flow over complex/moving boundaries, Comput. Fluids 140 (2016) 122–135.
[28]
L. Wang, C. Xie, W. Huang, A monolithic projection framework for constrained fsi problems with the immersed boundary method, Comput. Methods Appl. Mech. Eng. 371 (2020).
[29]
M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible 2-phase flow, J. Comput. Phys. 114 (1994) 146–159.
[30]
R.M. Beam, R.F. Warming, An implicit factored scheme for the compressible Navier-Stokes equations, AIAA J. 16 (1978) 393–402.
[31]
A.J. Chorin, The numerical solution of the Navier-Stokes equations for an incompressible fluid, Bull. Am. Math. Soc. 73 (1967) 928–931.
[32]
M.-C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160 (2000) 705–719.
[33]
R.P. Beyer, R.J. LeVeque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29 (1992) 332–364.
[34]
M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.d. New York University, United States – New York, 1998.
[35]
K. Kim, S.-J. Baek, H.J. Sung, An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations, Int. J. Numer. Methods Fluids 38 (2002) 125–138.
[36]
B.P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19 (1979) 59–98.
[37]
X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994) 200–212.
[38]
G.-S. Jiang, D. Peng, Weighted eno schemes for Hamilton–Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2126–2143.
[39]
M. Sussman, E. Fatemi, An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput. 20 (1999) 1165–1191.
[40]
J.A. Sethian, Fast marching methods, SIAM Rev. 41 (1999) 199–235.
[41]
H. Zhao, A fast sweeping method for Eikonal equations, Math. Comput. 74 (2005) 603–627.
[42]
Wang, L. (2019): OpFlow: EDSL for PDE solver composing. https://github.com/OpFlow-dev/OpFlow.
[43]
C.S. Peskin, The immersed boundary method, Acta Numer. 11 (2002) 479–517.
[44]
R.J. Leveque, Z.L. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput. 18 (1997) 709–735.
[45]
Z. Li, M.-C. Lai, The immersed interface method for the Navier–Stokes equations with singular forces, J. Comput. Phys. 171 (2001) 822–842.
[46]
T. Abadie, J. Aubin, D. Legendre, On the combined effects of surface tension force calculation and interface advection on spurious currents within volume of fluid and level set frameworks, J. Comput. Phys. 297 (2015) 611–636.
[47]
R. Bellman, R.H. Pennington, Effects of surface tension and viscosity on Taylor instability, Q. Appl. Math. 12 (1954) 151–162.
[48]
K. Yokoi, Efficient implementation of thinc scheme: a simple and practical smoothed vof algorithm, J. Comput. Phys. 226 (2007) 1985–2002.
[49]
B.J. Daly, Numerical study of the effect of surface tension on interface instability, Phys. Fluids 12 (2003) 1340.
[50]
H. Ding, P. Spelt, C. Shu, Diffuse interface model for incompressible two-phase flows with large density ratios, J. Comput. Phys. 226 (2007) 2078–2095.
[51]
G. Tryggvason, Numerical simulations of the Rayleigh-Taylor instability, J. Comput. Phys. 75 (1988) 253–282.
[52]
J.L. Guermond, L. Quartapelle, A projection fem for variable density incompressible flows, J. Comput. Phys. 165 (2000) 167–188.
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Published: 12 April 2024
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