Efficient multilevel restriction–prolongation expressions for hybrid finite volume element method

References

• Baliga, B.R., and Patankar, S.V., 1983. A control-volume finite element method for two dimensional fluid flow and heat transfer, Numerical Heat Transfer 6 (3) (1983), pp. 245–261.
   Google Scholar
• Blackwell, B.F., and Armaly, B.F., 1993. Computational aspects of heat transfer benchmark problems, The winter annual meeting of the ASME 258 (1993), HTD.
   Google Scholar
• Bramble, J.H., 1993. Multigrid methods. Harlow: Longman Scientific & Technical; 1993.
   Google Scholar
• Brandt, A., 1977. Multi-level adaptive solutions to boundary-value problems, Mathematics of Computation 31 (1977), pp. 333–390.
   Web of Science ®Google Scholar
• Caughey, D.A., 2005. Symmetric Gauss–Seidel multigrid solution of the Euler equations on structured and unstructured grids, International Journal of Computational Fluid Dynamics 19 (8) (2005), pp. 605–612.
   Web of Science ®Google Scholar
• Chan, K.I., and Ng, E.Y.K., 2003. Higher-order upwind distribution-formula scheme for structured and unstructured adaptive flow solvers, International Journal of Computational Fluid Dynamics 17 (1) (2003), pp. 61–73.
   Web of Science ®Google Scholar
• Cope, W.K., Wang, G., and Vanka, S.P., 1994. A staggered grid multilevel method for the simulation of fluid flow in 3-d complex geometries, (1994), AIAA paper 94-0778.
   Google Scholar
• Darbandi, M., Banaeizadeh, A., and Schneider, G.E., 2004. Parallel computation of a mixed convection problem using fully-coupled and segregated algorithms, American society of mechanical engineers, ASME heat transfer division, ASME-HTD 375 (1) (2004), pp. 313–322.
   Google Scholar
• Darbandi, M., and Bostandoost, S.M., 2005. A new formulation toward unifying the velocity role in collocated variable arrangement, Numerical Heat Transfer, Part B 47 (2005), pp. 1–22.
   Web of Science ®Google Scholar
• Darbandi, M., and Hosseinizadeh, S.F., 2003. General pressure-correction strategy to include density variation in incompressible algorithms, Journal of Thermophysics and Heat Transfer 17 (3) (2003), pp. 372–380.
   Web of Science ®Google Scholar
• Darbandi, M., and Hosseinizadeh, S.F., 2006. Numerical simulation of thermobuoyant flow with large temperature variation, Journal of Thermophysics and Heat Transfer 20 (2) (2006), pp. 285–296.
   Web of Science ®Google Scholar
• Darbandi, M., and Naderi, A.R., 2006. Multiblock hybrid grid finite volume method to solve flow in irregular geometries, Computer Methods in Applied Mechanics and Engineering 196 (2006), pp. 321–336.
   Web of Science ®Google Scholar
• Darbandi, M., and Schneider, G.E., 1998. Analogy-based method for solving compressible and incompressible flows, Journal of Thermophysics and Heat Transfer 2 (12) (1998), pp. 239–247.
   Web of Science ®Google Scholar
• Darbandi, M., and Schneider, G.E., 1999. Application of an all-speed flow algorithm to heat transfer problems, Numerical Heat Transfer 35 (1999), pp. 695–715.
   Web of Science ®Google Scholar
• Darbandi, M., and Schneider, G.E., 2003. Thermobuoyancy treatment for electronic packaging using an improved advection scheme, Journal of Electronic Packaging 125 (2003), pp. 224–250.
   Web of Science ®Google Scholar
• Darbandi, M., Schneider, G.E., and Vakili, S., 2006. Performance of different preconditioned Krylov subspace methods to solve fully coupled fluid flow equations, Computational Fluid Dynamics Journal 15 (1) (2006), pp. 35–43.
   Google Scholar
• Darbandi, M., and Vakilipour, S., 2007. Using fully implicit conservative statements to close open boundaries passing through recirculations, International Journal for Numerical Methods in Fluids 53 (3) (2007), pp. 371–389.
   Web of Science ®Google Scholar
• Darbandi, M., Zakyani, M., et al., 2006. "Solving turbulent flow in curvilinear coordinate system using covariant velocity calculation procedure". In: Liu, G.R., ed. Computational methods. The Netherlands: Springer; 2006. pp. 161–175, In:.
   Google Scholar
• Darmofal, D.L., and Siu, K., 1999. A robust multigrid algorithm for the Euler equations with local preconditioning and semi-coarsening, Journal of Computational Physics 151 (1999), pp. 728–756.
   Web of Science ®Google Scholar
• Drikakis, D., Iliev, O.P., and Vassileva, D.P., 1998. A nonlinear multigrid method for three-dimensional incompressible Navier–Stokes equations, Journal of Computational Physics 146 (1998), pp. 301–321.
   Web of Science ®Google Scholar
• Gjesdal, T., 1996. A note on the additive correction multigrid method, International Communications in Heat and Mass Transfer 23 (2) (1996), pp. 293–298.
   Web of Science ®Google Scholar
• Karimian, S.M.H., and Schneider, G.E., 1995. Pressure based control-volume finite-element method for flow at all speeds, AIAA Journal 33 (9) (1995), pp. 1611–1618.
   Web of Science ®Google Scholar
• Kondo, N., and Matsukuma, D., 2005. Three-dimensional computation for flow around two circular cylinders in side-by-side arrangement by a third-order upwind finite element method, International Journal of Computational Fluid Dynamics 19 (1) (2005), pp. 37–43.
   Web of Science ®Google Scholar
• Kotakemori, H., Niki, H., and Okamoto, N., 2004. A two-step preconditioning method for solving dense linear systems, International Journal of Computational Fluid Dynamics 18 (1) (2004), pp. 93–99.
   Web of Science ®Google Scholar
• Lavery, N., and Taylor, C., 1999. Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow, International Journal for Numerical Methods in Fluids 30 (1999), pp. 609–634.
   Web of Science ®Google Scholar
• Masson, C., Saabas, H.J., and Baliga, B.R., 1994. Co-located equal order finite-volume finite-element method for two dimensional axisymmetric compressible fluid flow, International Journal of Numerical Methods in Fluids 18 (1994), pp. 12–26.
   Web of Science ®Google Scholar
• Naterer, G.F., 2003. Eulerian three-phase formulation with coupled droplet flow and multimode heat transfer, Numerical Heat Transfer B 43 (2003), pp. 331–352.
   Web of Science ®Google Scholar
• Ogedengbe, E.O.B., and Naterer, G.F., 2007. Convective flux dependence on upstream flow directionality in finite-volume computations, Numerical Heat Transfer A 51 (2007), pp. 617–633.
   Web of Science ®Google Scholar
• Paillère, H., Le Quéré, P., Weisman, C., Vierendeels, J., Dick, E., Braack, M., Dabbene, F., Beccantini, A., Studer, E., Kloczko, T., Corre, C., Heuveline, V., Darbandi, M., and Hosseinizadeh, S.F., 2005. Modelling of natural convection flows with large temperature differences: a benchmark problem for low mach number solvers, part 2, ESAIM: Mathematical Modelling and Numerical Analysis 39 (2005), pp. 617–621.
   Web of Science ®Google Scholar
• Patankar, S.V., 1980. Numerical heat transfer and fluid flow. Washington, DC: Hemisphere; 1980.
   Google Scholar
• Raithby, G.D., 1976. Skew upstream differencing schemes for problems involving fluid flow, Computer Methods in Applied Mechanics and Engineering 9 (1976), pp. 153–164.
   Google Scholar
• Rhie, C.M., and Chow, W.L., 1983. Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA Journal 21 (11) (1983), pp. 1525–1532.
   Web of Science ®Google Scholar
• Saabas, H.J., and Baliga, B.R., 1994. Co-located equal order control volume finite element method for multidimensional incompressible fluid flow – part I: formulation, Numerical Heat Transfer 26 (1994), pp. 381–407.
   Web of Science ®Google Scholar
• Sakakihara, M., Morimoto, M., Niki, H., and Okamoto, N., 2004. Preconditioned iterative methods for linear equations arising from the boundary element method, International Journal of Computational Fluid Dynamics 18 (8) (2004), pp. 625–630.
   Web of Science ®Google Scholar
• Schneider, G.E., 1987. "Elliptic systems: finite-element method I". In: Minkowycz, W.J., Sparrow, E.M., Schneider, G.E., and Pletcher, R.H., eds. Handbook of numerical heat transfer. Washington, DC: Hemisphere; 1987. pp. 379–420, In.
   Google Scholar
• Schneider, G.E., and Raw, M.J., 1987. Control volume finite element method for heat transfer and fluid flow using colocated variables – 1. Computational procedure, Numerical Heat Transfer 11 (4) (1987), pp. 363–390.
   Web of Science ®Google Scholar
• Schneider, G.E., and Zedan, M., 1983. Control-volume finite element method formulation of the heat conduction equation, Spacecraft Thermal Control, Design and Operation 36 (1983), pp. 305–326.
   Google Scholar
• Schreck, E., and Peric, M., 1993. Computation of fluid flow with a parallel multigrid solver, International Journal for Numerical Methods in Fluids 16 (1993), pp. 303–327.
   Web of Science ®Google Scholar
• Versteeg, H.K., and Malalasekera, W., 1995. An introduction to computational fluid dynamics: the finite volume method. Harlow: Longman; 1995.
   Google Scholar
• Wapperom, P., and Webster, M.F., 1999. Simulation for viscoelastic flow by a finite volume/element method, Computer Methods in Applied Mechanics and Engineering 180 (1999), pp. 281–304.
   Web of Science ®Google Scholar
• Warendorf, K., Kuster, U., and Ruhle, R., 1999. Upwind prolongation for a highly unstructured Euler solver, Proceedings of the sixth European multigrid conference held in Gent (1999), pp. 271–277, Belgium.
   Google Scholar