We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.
|Original language||English (US)|
|Number of pages||24|
|Journal||Journal of Computational Physics|
|State||Published - Feb 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): 42959
Acknowledgements: Research supported in part by ONR N00014-09-1-0101, ONR N00014-11-1-0027, ONR N00014-06-1-0505, ONR N00014-05-1-0479, for a computing cluster, NSF IIS-1048573, and King Abdullah University of Science and Technology (KAUST) 42959. C.S. was supported in part by a Stanford Graduate Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.