Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics
A Sequential Regularization Method for Time-Dependent Incompressible Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Computation of multiphase systems with phase field models
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
A continuous surface tension force formulation for diffuse-interface models
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
New finite-element/finite-volume level set formulation for modelling two-phase incompressible flows
Journal of Computational Physics
A conservative level set method for two phase flow II
Journal of Computational Physics
Diffuse interface model for incompressible two-phase flows with large density ratios
Journal of Computational Physics
Short note: A new contact line treatment for a conservative level set method
Journal of Computational Physics
Hi-index | 31.45 |
A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into account for the level set function so that a sharply varying interface can be stably predicted. To preserve the conservative property, the mapping given by @x@?=x@?-u@?t is performed between two coordinates x@? and @x@? for the advection-diffusion equation in a flow field with velocity u. To capture the interface, the flux term capable of compressing the level set contours is also adopted in the construction of linear inviscid Burgers' equation, which is indispensable in the level set method. To resolve the physically sharp interface without incurring contact discontinuity oscillations, a damping term which is nonlinear in terms of the level set function and can render an adequate artificial diffusion to stabilize the contact surface is added into the reinitialization step in the modified level set method. For accurately predicting the level set function, the advection scheme for solving the linear inviscid Burgers' equation in the advection step of the modified level set method is developed to accommodate the true dispersion relation. The solution computed from the resulting two-dimensional dispersion-relation-preserving advection scheme can minimize the phase error. Less artificial damping is needed to damp the oscillations in the vicinity of contact surface and the interface can be less numerically smeared. For the sake of programming simplicity, the incompressible two-phase flow will be discretized in non-staggered grids without incurring checkerboard oscillations by the developed explicit compact scheme for the approximation of pressure gradient terms. For the verification of the proposed two-dimensional dispersion-relation-preserving scheme and the non-staggered incompressible flow solver, three benchmark problems have been chosen in this study. The proposed conservative level set method for capturing the interface in incompressible fluid flows is also verified by solving the dam-break, bubble rising in water, droplet falling in water and Rayleigh-Taylor instability problems. Good agreements with the referenced solutions are demonstrated for all the four investigated problems.