Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
Computation of multiphase systems with phase field models
Journal of Computational Physics
De-aliasing on non-uniform grids: algorithms and applications
Journal of Computational Physics
Short note: Spontaneous shrinkage of drops and mass conservation in phase-field simulations
Journal of Computational Physics
An efficient moving mesh spectral method for the phase-field model of two-phase flows
Journal of Computational Physics
An unconditionally stable rotational velocity-correction scheme for incompressible flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
An eigen-based high-order expansion basis for structured spectral elements
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase-field framework for dealing with two-phase outflows or open boundaries. The set of two-phase outflow boundary conditions for the phase-field and flow variables are designed to prevent the un-controlled growth in the total energy of the two-phase system, even in situations where strong backflows or vortices may be present at the outflow boundaries. We also present an additional boundary condition for the phase field function, which together with the usual Dirichlet condition can work effectively as the phase-field inflow conditions. The numerical algorithm for dealing with these boundary conditions is developed on top of a strategy for de-coupling the computations of all flow variables and for overcoming the performance bottleneck caused by variable coefficient matrices associated with variable density/viscosity. The algorithm contains special constructions, for treating the variable dynamic viscosity in the outflow boundary condition, and for preventing a numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests with incompressible two-phase flows involving inflow and outflow boundaries demonstrate that, the two-phase outflow boundary conditions and the numerical algorithm developed herein allow for the fluid interface and the two-phase flow to pass through the outflow or open boundaries in a smooth and seamless fashion, and that our method produces stable simulations when large density ratios and large viscosity ratios are involved and when strong backflows are present at the outflow boundaries.