This article analyses the generation of ‘optimal’ grids for lubrication problems including hydrodynamic and elastohydrodynamic lubrication. It does this by using existing numerical solutions on (very) fine and regular grids, and studying the coarse grids generated by algebraic multigrid. This article analyses two hydrodynamic lubrication applications, the circular hydrodynamic lubrication contact and the rough surface lubrication. The latter subject is currently attracting a large interest from both industry and university. A third elastohydrodynamic lubrication application highlights the strong coupling in the high-pressure zone.
DowsonDHigginsonGR. Elastohydrodynamic lubrication: the fundamentals of roller and gear lubrication. Oxford, Great Britain: Pergamon Press, 1966.
2.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts, part I: Theoretical Formulation. ASME J Lub Technol1976; 98: 223–229.
3.
KudishIICovitchMJ. Modeling and analytical methods in tribology. Boca Raton, FL: Chapman and Hall/CRC press, 2010.
4.
BrandtA. Multi-level adaptive solutions to boundary value problems. Math Comp1977; 31: 333–390.
5.
LubrechtAAten NapelWEBosmaR. Multigrid, an alternative method of solution for two-dimensional elastohydrodynamically lubricated point contact calculations. ASME J Tribol1987; 109: 437–443.
6.
RugeJStübenK. Algebraic Multigrid (AMG). In: McCormickSF (ed.) In: Multigrid methods. Philadelphia: SIAM, Frontiers in Applied Mathematics, 1987, pp. 169–212.
7.
VennerCHLubrechtAA. MultiLevel methods in lubrication, vol. 37, USA, Elsevier: Tribology Series, 2000, p.379.
8.
TrottenbergUOosterleeCSchuellerA. Multigrid. San Diego, USA: Academic Press, 2001.
9.
WesselingP. An introduction to multigrid methods. Flourtown, USA: R.T. Edwards, Inc, 2004.
10.
BriggsWLEmden HensonVMcCormickS. A multigrid tutorial, 2nd ed. US: SIAM, 2007.
11.
BrandtA. Algebraic Multigrid Theory: The symmetric case. Appl Math Comput1986; 19(1-4): 23–56.
12.
BrandtA. General highly accurate algebraic coarsening. Electronic Trans Numer Anal2000; 10: 120–120.
13.
FalgoutRDBrannickJBrezinaM. J. Phys Conf Series2005; 16: 456–460.
14.
ManteuffelTMcCormickSParkMRugeJ. Operator-based interpolation for bootstrap algebraic multigrid. Numer Linear Algebra Appl2010; 17(2-3): 519–537.
15.
AlcouffeREBrandtADendyJEPainterJW. The multigrid methods for the diffusion equation with strongly discontinuous coefficients. SIAM J Sci Stat Comput1981; 2: 430–454.
16.
DendyJE. Black box multigrid for nonsymmetric problems. Appl Math Comput1982; 13: 261–284.
17.
VennerCHten NapelWE. Multilevel solution of the EHL circular contact problem, part 1: Theory and numerical algorithm. Wear1992; 152: 351–367.
