SIAM Journal on Scientific and Statistical Computing
A continuum method for modeling surface tension
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Composite Step Product Methods for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Domain decomposition based $${\mathcal H}$$-LU preconditioning
Numerische Mathematik
Error Bounds for Least Squares Gradient Estimates
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
In multifluid problems with surface tension the fluid pressure and its derivative are discontinuous at fluid interfaces. We present a Cartesian grid embedded boundary method for numerically resolving these discontinuities in which we use Neumann-Neumann preconditioned iterative substructuring to solve the governing equations. We validate this method by computing several well-known Poisson problems with discontinuous coefficients, and we compare its performance to an approach based on simple iteration. By analogy with the conjugate gradient method, we hypothesize that the scaling of the Neumann-Neumann preconditioned iterative substructuring is O(h^-^Dlnh^-^1) where h is the cell size and D=2,3 is the dimensionality of the problem. In contrast, we show that the simple iterative procedure scales like O(h^-^(^D^+^1^)) and is slower by a factor of 4000 for a small (i.e., 64x64 cell) model calculation with physical parameters corresponding to a 1.5mm air bubble in water. We present an analytical model to explain the scaling of this iterative procedure.