[1] Ranjith, D.J., Sreenath, K., Ajith, K.S., Studies on vortex structures formed inside a lid-driven cavity—Influence of extending the length of the cavity, IOP Conference Series: Materials Science and Engineering, 577(1), 2019, 012134.
[2] Ding, P., Solution of lid-driven cavity problems with an improved SIMPLE algorithm at high Reynolds numbers, International Journal of Heat and Mass Transfer, 115, 2017, 942–954.
[3] Narain, J.P., Lid driven cavity flow: Review and future trends, American Journal of Fluid Dynamics, 2022(1), 2022, 1–15.
[4] Zhang, T., Shi, B., Chai, Z., Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities, Computers & Fluids, 39(10), 2010, 1977–1989.
[5] González, L.M., Ahmed, M., Kühnen, J., Three-dimensional flow instability in a lid-driven isósceles triangular cavity, Journal of Fluid Mechanics, 675, 2011, 369–396.
[6] Glowinski, R., Guidoboni, G., Pan, T.W., Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity, Journal of Computational Physics, 216(1), 2006, 76–91.
[7] Pepper, D.W., Wang, X., Carrington, D.B., A meshless method for modeling convective heat transfer, Journal of Heat Transfer, 135(1), 2013, 1–9.
[8] Ding, Y., Kawahara, M., Linear stability of incompressible fluid flow in a cavity using finite element method, International Journal for Numerical Methods in Fluids, 27(1–4), 1998, 139–157.
[9] Poochinapan, K., Numerical implementations for two-dimensional lid driven cavity flow in stream function formulation, ISRN Applied Mathematics, 2012, 1–17.
[10] Merle, X., Alizard, F., Robinet, J.C., Finite difference methods for viscous incompressible global stability analysis, Computers & Fluids, 39(6), 2010, 911–925.
[11] Erturk, E., Discussions on driven cavity flow, International Journal for Numerical Methods in Fluids, 60, 2009, 275–294.
[12] Arumuga, P.D., Dass, A.K., Simulation of incompressible flows in two-sided lid driven square cavities. Part I – Finite difference method, CFD Letters, 2(1), 2010, 13–24.
[13] Arumuga, P.D., Dass, A.K., Simulation of flow in two-sided lid driven square cavities by the lattice Boltzmann method, WIT Transactions on Engineering Sciences, 59, 2008, 45–54.
[14] Lin, L.S., Chen, Y.C., Lin, C.A., Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios, Computers & Fluids, 45(1), 2011, 233–240.
[15] Shamekhi, A., Sadeghy, K., Lid driven cavity simulation by mesh‐free method, International Journal of Computational Methods, 4(3), 2007, 397–415.
[16] Sahin, M., Owens, R.G., A novel fully implicit finite volume method applied to the lid driven cavity problem. Part II. Linear stability analysis, International Journal for Numerical Methods in Fluids, 42(1), 2003, 79–88.
[17] Bruneau, C.H., Saad, M., The two-dimensional lid driven cavity problem revisited, Computers & Fluids, 35(3), 2006, 326–348.
[18] Mawarsih, E., Budiana, E.P., Yuana, K.A., et al., Simulation of lid driven cavity with top and bottom moving boundary conditions using implicit finite difference method and staggered grid, AIP Conference Proceedings, East Java, Indonesia, 2021.
[19] Gutt, R., Groşan, T., On the lid driven problem in a porous cavity: A theoretical and numerical approach, Applied Mathematics and Computation, 266, 2015, 1070–1082.
[20] Budiana, E.P., Indarto, I., Deendarlianto, D., et al., Numerical study of meshless radial basis functions in the lid driven cavity problem, AIP Conference Proceedings, East Java, Indonesia, 2021.
[21] Ferrari, D., Dumbser, M., A semi-implicit finite volume scheme for incompressible two phase flows, Communications in Applied Mathematics and Computation, 6, 2024, 2295-2330.
[22] Budiana, E.P., Pranowo, Indarto, et al., Meshless numerical model based on radial basis function method to simulate the Rayleigh–Taylor instability, Computers & Fluids, 201, 2020, 104472.
[23] Ghia, U., Ghia, K.N., Shin, C.T., High Reynolds number solutions for incompressible flow using the Navier–Stokes equations and a multigrid method, Journal of Computational Physics, 48(3), 1982, 387–411.
[24] Erturk, E., Gökçöl, C., Fourth order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids, 50(4), 2006, 421–436.
[25] Salih, A., Streamfunction–vorticity formulation, Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram, 2013, 1-10.
[26] Chyczewski, T.S., Marconi, F., Solution of the Euler and Navier–Stokes equations on parallel processors using a transposed/Thomas ADI algorithm, Proceedings of the 11th Computational Fluid Dynamics Conference, Orlando, United States of America, 1993, 144–154.
[27] Pulliam, T.H., Zingg, D.W., Fundamental Algorithms in Computational Fluid Dynamics, Springer Nature, New York, 2014.
[28] Rusli, N., Kasiman, E.H., Numerical computation of a two-dimensional Navier–Stokes equation using an improved finite difference method, Matematika, 27(1), 2011, 1–9.
[29] Aeran, A., Lemu, H.G., Time integration schemes in dynamic problems: Effect of damping on numerical stability and accuracy, International Workshop on Advanced Manufacturing Automation, Manchester, England, 2016.
[30] Krieg, R.D., Unconditional stability in numerical time integration methods, Journal of Applied Mechanics, 40(2), 1973, 417–421.
[31] Hoffmann, K., Chiang, S., Computational Fluid Dynamics Volume I, Engineering Education Systems, Kansas, 2000.
[32] Nie, B.D., Cao, B.Y., Three mathematical representations and an improved ADI method for hyperbolic heat conduction, International Journal of Heat and Mass Transfer, 135, 2019, 974–984.
[33] Rogers, S.E., Kwak, D., Kiris, C., Numerical solution of the incompressible Navier–Stokes equations for steady state and time dependent problems, Australian Fluid Mechanic Conference, Melbourne, Austalia,1994, 463.
[34] Septiyanto, M.D., Budiana, E.P., Hadi, S., A novel RBF DDM method for modeling transient droplet spreading in simple oil shear flow, Engineering Analysis with Boundary Elements, 171, 2025, 106099.
[35] Spotz, W.F., High order compact finite difference schemes for computational mechanics, Ph.D. Thesis, Faculty of The Graduate School, The University of Texas, Austin, USA, 1995.
[36] Khorasanizade, S., Sousa, J.M.M., A detailed study of lid driven cavity flow at moderate Reynolds numbers using incompressible smoothed particle hydrodynamics, International Journal for Numerical Methods in Fluids, 76(10), 2014, 653–668.
[37] Mendu, S.S., Das, P.K., Fluid flow in a cavity driven by an oscillating lid: A simulation by the lattice Boltzmann method, European Journal of Mechanics – B/Fluids, 39, 2013, 59–70.
[38] Mulbah, C., Kang, C., Mao, N., Zhang, W., Shaikh, A.R., Teng, S., A review of volume of fluid methods for simulating bubble dynamics, Progress in Nuclear Energy, 154, 2022, 104478.
[39] Zhang, S., Hu, X., Lourenço, S.D.N., Modeling of water droplet dynamics on hydrophobic soils: A review, E3S Web of Conferences, Milos Island, Greece 18005, 2023, 1–6.
[40] Mohammadi, M., Shafiei, M., Zarin, T., Kazemzadeh, Y., Parsaei, R., Riazi, M., Investigation of smoothed particle hydrodynamics method for modeling two phase flow through porous medium: Application for drainage and imbibition processes, Scientific Reports, 14(1), 2024, 22144.
[41] Jones, I.P., Thompson, C.P., On the use of nonuniform grids in finite difference calculations, No. AERE-R-9765, 1980, 1-31.
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