[
1. E. Ferrer and R. Willden, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, vol. 15, pp. 1787–1806, 1972.
]Search in Google Scholar
[
2. C. Taylor and P. Hood, A numerical solution of the Navier-Stokes equations using the finite element technique, Computers and Fluids, vol. 1, pp. 73–100, 1973.10.1016/0045-7930(73)90027-3
]Search in Google Scholar
[
3. A. Brooks and T. Hughes, Stream-line upwind/Petrov Galerkin formulstion for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation, Computer Methods in Applied Mechanics and Engineering, vol. 32, pp. 199–259, 1982.10.1016/0045-7825(82)90071-8
]Search in Google Scholar
[
4. T. Hughes, M. Mallet, and M. Mizukami, A new finite element formulation for computational fluid dynamics: II. Beyond SUPG, Computer Methods in Applied Mechanics and Engineering, vol. 54, pp. 341–355, 1986.10.1016/0045-7825(86)90110-6
]Search in Google Scholar
[
5. M. Fortin, Old and new finite elements for incompressible flows, International Journal for Numerical Methods in Fluids, vol. 1, pp. 347–364, 1981.10.1002/fld.1650010406
]Search in Google Scholar
[
6. R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II, Numerische Mathematik, vol. 59, pp. 615–636, 1991.10.1007/BF01385799
]Search in Google Scholar
[
7. J. G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes Problem. I. Regularity of solutions and second order error estimates for spatial discretization, SIAM Journal on Numerical Analysis, vol. 19, pp. 275–311, 1982.10.1137/0719018
]Search in Google Scholar
[
8. J. G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes Problem. III. Smoothing property and higher order error estimates for spatial discretization, SIAM Journal on Numerical Analysis, vol. 25, pp. 489–512, 1988.10.1137/0725032
]Search in Google Scholar
[
9. F. Harlow and J. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface, Physics of Fluids, vol. 8, pp. 2182–2189, 1965.10.1063/1.1761178
]Search in Google Scholar
[
10. V. Patankar and B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, vol. 15, pp. 1787–1806, 1972.10.1016/0017-9310(72)90054-3
]Search in Google Scholar
[
11. S. Patankar, Numerical heat transfer and fluid flow. New York: McGraw-Hill, 1980.
]Search in Google Scholar
[
12. J. van Kan, A second-order accurate pressure correction method for viscous incompressible flow, SIAM Journal on Scientific and Statistical Computing, vol. 7, pp. 870–891, 1986.10.1137/0907059
]Search in Google Scholar
[
13. F. Bassi, A. Crivellini, D. D. Pietro, and S. Rebay, An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows, Computers and Fluids, vol. 36, pp. 1529–1546, 2007.10.1016/j.compfluid.2007.03.012
]Search in Google Scholar
[
14. K. Shahbazi, P. F. Fischer, and C. R. Ethier, A high-order discontinuous galerkin method for the unsteady incompressible navier-stokes equations, Journal of Computational Physics, vol. 222, pp. 391–407, 2007.10.1016/j.jcp.2006.07.029
]Search in Google Scholar
[
15. E. Ferrer and R. Willden, A high order Discontinuous Galerkin Finite Element solver for the incompressible Navier-Stokes equations, Computer and Fluids, vol. 46, pp. 224–230, 2011.10.1016/j.compfluid.2010.10.018
]Search in Google Scholar
[
16. N. Nguyen, J. Peraire, and B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol. 230, pp. 1147–1170, 2011.10.1016/j.jcp.2010.10.032
]Search in Google Scholar
[
17. S. Rhebergen and B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, Journal of Computational Physics, vol. 231, pp. 4185–4204, 2012.10.1016/j.jcp.2012.02.011
]Search in Google Scholar
[
18. S. Rhebergen, B. Cockburn, and J. J. van der Vegt, A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol. 233, pp. 339–358, 2013.10.1016/j.jcp.2012.08.052
]Search in Google Scholar
[
19. A. Crivellini, V. D’Alessandro, and F. Bassi, High-order discontinuous Galerkin solutions of three-dimensional incompressible RANS equations, Computers and Fluids, vol. 81, pp. 122–133, 2013.10.1016/j.compfluid.2013.04.016
]Search in Google Scholar
[
20. B. Klein, F. Kummer, and M. Oberlack, A SIMPLE based discontinuous Galerkin solver for steady incompressible flows, Journal of Computational Physics, vol. 237, pp. 235–250, 2013.10.1016/j.jcp.2012.11.051
]Search in Google Scholar
[
21. A. Chorin, A numerical method for solving incompressible viscous flow problems, Journal of Computational Physics, vol. 2, pp. 12–26, 1967.10.1016/0021-9991(67)90037-X
]Search in Google Scholar
[
22. F. Bassi, A. Crivellini, D. D. Pietro, and S. Rebay, On a robust discontinuous Galerkin technique for the solution of compressible flow, Journal of Computational Physics, vol. 218, pp. 208–221, 2006.10.1016/j.jcp.2006.03.006
]Search in Google Scholar
[
23. V. Casulli, Semi-implicit finite difference methods for the two–dimensional shallow water equations, J. Comp. Phys., vol. 86, pp. 56–74, 1990.10.1016/0021-9991(90)90091-E
]Search in Google Scholar
[
24. V. Casulli and R. Cheng, Semi-implicit finite difference methods for three-dimensional shallow water flow, Int. J. Numer. Methods Fluids, vol. 15, pp. 629–648, 1992.10.1002/fld.1650150602
]Search in Google Scholar
[
25. M. Tavelli and M. Dumbser, A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes, J. Comp. Phys., vol. 319, pp. 294–323, 2016.10.1016/j.jcp.2016.05.009
]Search in Google Scholar
[
26. U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math., vol. 25, pp. 151–167, 1982.10.1016/S0168-9274(97)00056-1
]Search in Google Scholar
[
27. S. Boscarino and L. Pareschi, On the asymptotic properties of IMEX Runge-Kutta schemes for hyperbolic balance laws, Journal of Computational and Applied Mathematics, vol. 316, pp. 60–73, 2017.10.1016/j.cam.2016.08.027
]Search in Google Scholar
[
28. S. Boscarino and G. Russo, On a class of uniformly accurate IMEX Runge-Kutta schemes and applications to hyperbolic systems with relaxation, SIAM J. Sci. Comput., vol. 31, pp. 1926–1945, 2009.10.1137/080713562
]Search in Google Scholar
[
29. L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., vol. 25, pp. 129–155, 2005.10.1007/s10915-004-4636-4
]Search in Google Scholar
[
30. S. Boscarino, L. Pareschi, and G. Russo, A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation, SIAM J. Numer. Anal., vol. 55, no. 4, pp. 2085–2109, 2017.10.1137/M1111449
]Search in Google Scholar
[
31. W. Boscheri, G. Dimarco, R. Loubère, M. Tavelli, and M. Vignal, A second order all Mach number IMEX finite volume solver for the three dimensional Euler equations, J. Comp. Phys., vol. 415, p. 109486, 2020.10.1016/j.jcp.2020.109486
]Search in Google Scholar
[
32. W. Boscheri, G. Dimarco, and M. Tavelli, An efficient second order all Mach finite volume solver for the compressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, vol. 374, p. 113602, 2021.10.1016/j.cma.2020.113602
]Search in Google Scholar
[
33. V. DeCaria and M. Schneier, An embedded variable step IMEX scheme for the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, vol. 376, p. 113661, 2021.10.1016/j.cma.2020.113661
]Search in Google Scholar
[
34. F. Meng, J. Banks, W. Henshaw, and D. Schwendeman, Fourth-order accurate fractional-step IMEX schemes for the incompressible Navier-Stokes equations on moving overlapping grids, Computer Methods in Applied Mechanics and Engineering, vol. 366, p. 113040, 2020.10.1016/j.cma.2020.113040
]Search in Google Scholar
[
35. W. Wang, Z. Wang, and M. Mao, Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations, Applied Numerical Mathematics, vol. 172, pp. 393–412, 2022.10.1016/j.apnum.2021.10.019
]Search in Google Scholar
[
36. A. Larios, L. G. Rebholz, and C. Zerfas, Global in time stability and accuracy of imex-fem data assimilation schemes for navier-stokes equations, Computer Methods in Applied Mechanics and Engineering, vol. 345, pp. 1077–1093, 2019.10.1016/j.cma.2018.09.004
]Search in Google Scholar
[
37. W. Boscheri and L. Pareschi, High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers, J. Comp. Phys., vol. 434, p. 110206, 2021.10.1016/j.jcp.2021.110206
]Search in Google Scholar
[
38. D. Levy, G. Puppo, and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, M2AN Math. Model. Numer. Anal., vol. 33, no. 3, pp. 547–571, 1999.10.1051/m2an:1999152
]Search in Google Scholar
[
39. F. Fambri and M. Dumbser, Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids, Applied Numerical Mathematics, vol. 110, pp. 41–74, 2016.10.1016/j.apnum.2016.07.014
]Search in Google Scholar
[
40. A. Stroud, Approximate Calculation of Multiple Integrals. Englewood Cliffs, New Jersey: Prentice-Hall Inc., 1971.
]Search in Google Scholar
[
41. V. Casulli, A semi-implicit finite difference method for non-hydrostatic free-surface flows, Int. J. Num. Meth. in Fluids, vol. 30, pp. 425–440, 1999.10.1002/(SICI)1097-0363(19990630)30:4<425::AID-FLD847>3.0.CO;2-D
]Search in Google Scholar
[
42. B. Einfeldt, C. Munz, P. Roe, and B. Sjögreen, A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers, J. Comp. Phys., vol. 341, pp. 341–376, 2017.10.1016/j.jcp.2017.03.030
]Search in Google Scholar
[
43. S. Boscarino, F. Filbet, and G. Russo, High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations, J. Sci. Comput., vol. 68, pp. 975–1001, 2016.10.1007/s10915-016-0168-y
]Search in Google Scholar
[
44. C.-W. Shu, High-order finite difference and finite volume weno schemes and discontinuous galerkin methods for cfd, International Journal of Computational Fluid Dynamics, vol. 17, no. 2, pp. 107–118, 2003.10.1080/1061856031000104851
]Search in Google Scholar
[
45. Y. Saad and M. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., vol. 7, pp. 856–869, 1986.10.1137/0907058
]Search in Google Scholar
[
46. J. Bell, P. Coletta, and H. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., vol. 85, pp. 257–283, 1989.10.1016/0021-9991(89)90151-4
]Search in Google Scholar
[
47. M. Dumbser, I. Peshkov, E. Romenski, and O. Zanotti, High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids, Journal of Computational Physics, vol. 314, pp. 824–862, 2016.10.1016/j.jcp.2016.02.015
]Search in Google Scholar
[
48. W. Boscheri, M.Dumbser, M.Ioriatti, I.Peshkov, and E.Romenski, A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics, Journal of Computational Physics, vol. 424, p. 109866, 2021.10.1016/j.jcp.2020.109866
]Search in Google Scholar
[
49. U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using Navier-Stokes equations and multigrid method, Journal of Computational Physics, vol. 48, pp. 387–411, 1982.10.1016/0021-9991(82)90058-4
]Search in Google Scholar
[
50. V. Casulli, A semi-implicit numerical method for the free-surface Navier-Stokes equations, Int. J. Numer. Methods Fluids, vol. 74, pp. 605–622, 2014.10.1002/fld.3867
]Search in Google Scholar
[
51. W. Boscheri, A space-time semi-Lagrangian advection scheme on staggered Voronoi meshes applied to free surface flows, Computers & Fluids, vol. 202, p. 104503, 2020.10.1016/j.compfluid.2020.104503
]Search in Google Scholar
[
52. M. Tavelli, W. Boscheri, G. Stradiotti, G. R. Pisaturo, and M. Righetti, A mass-conservative semi-implicit volume of fluid method for the navier-stokes equations with high order semi-lagrangian advection scheme, Computers and Fluids, p. 105443, 2022.10.1016/j.compfluid.2022.105443
]Search in Google Scholar