GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Vertex-centered and cell-centered multigrid for interface problems
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A numerical method for three-dimensional gas-liquid flow computations
Journal of Computational Physics
Journal of Computational Physics
Multi-physics treatment in the vicinity of arbitrarily deformable gas-liquid interfaces
Journal of Computational Physics
Journal of Computational Physics
An accurate adaptive solver for surface-tension-driven interfacial flows
Journal of Computational Physics
A Newton-Krylov Solver for Remapping-Based Volume-of-Fluid Methods
SIAM Journal on Scientific Computing
A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow
SIAM Journal on Scientific Computing
Interface curvature via volume fractions, heights, and mean values on nonuniform rectangular grids
Journal of Computational Physics
Estimating curvature from volume fractions
Computers and Structures
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, three improvements for modelling surface tension-dominated interfacial flows using interface tracking-based solution algorithms are presented. We have developed an improved approach to curvature estimation for incorporation into modern mesh-based surface tension models such as the Continuum Surface Force (CSF) and Sharp Surface Force (SSF) models. The scheme involves generating samples of curvature estimates from the multitude of height functions that can be generated from VOF representations of interfaces, and applying quality statistics based on interface orientation and smoothness to choose optimal candidates from the samples. In this manner, the orientation-dependence of past schemes for height function-based curvature estimation is ameliorated, the use of compact stencils for efficient computation can be maintained, and robustness is enhanced even in the presence of noticeable subgrid-scale disturbances in the interface representation. For surface tension-dominated flows, the explicit capillary timestep restriction is relaxed through timescale-separated slope limiting that identifies spurious modes in curvature evolution and omits them from contributing to surface force computations, thus promoting efficiency in simulation through the use of less timesteps. Efficiency in flow simulation is further promoted by incorporating awareness of interface location into multigrid preconditioning for Krylov subspace-based solution of elliptic problems. This use of interface-cognizance in solving problems such as the Helmholtz equation and the Poisson equation enables multigrid-like convergence in discontinuous-coefficient elliptic problems without the expense of constructing the Galerkin coarse-grid operator. The key improvements in the surface tension modelling and the numerical linear algebra are also applicable to level-set-based interfacial flow simulation.