Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
How to discretize the pressure gradient for curvilinear MAC grids
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature
SIAM Journal on Scientific Computing
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
A moving mesh method for the solution of the one-dimensional phase-field equations
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Variational mesh adaptation II: error estimates and monitor functions
Journal of Computational Physics
Journal of Computational Physics
Moving mesh methods with locally varying time steps
Journal of Computational Physics
Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
Journal of Computational Physics
A simple moving mesh method for one-and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
A phase field model which describes the motion of mixtures of two incompressible fluids is presented by Liu and Shen [C. Liu, J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method, Phys. D 179 (2003) 211-228]. The model is based on an energetic variational formulation. In this work, we develop an efficient adaptive mesh method for solving a phase field model for the mixture flow of two incompressible fluids. It is a coupled nonlinear system of Navier-Stokes equations and Allen-Cahn phase equation (phase-field equation) through an extra stress term and the transport term. The numerical strategy is based on the approach proposed by Li et al. [R. Li, T. Tang, P.-W. Zhang, Moving mesh methods in multiple dimensions based on harmonic maps, J. Comput. Phys. 170 (2001) 562-588] to separate the mesh-moving and PDE evolution. In the PDE evolution part, the phase-field equation is numerically solved by a conservative scheme with a Lagrange multiplier, and the coupled incompressible Navier-Stokes equations are solved by the incremental pressure-correction projection scheme based on the semi-staggered grid method. In the mesh-moving part, the mesh points are iteratively redistributed by solving the Euler-Lagrange equations with a parameter-free monitor function. In each iteration, the pressure and the phase are updated on the resulting new grid by a conservative-interpolation formula, while the velocity is re-mapped in a non-conservative approach. A simple method for preserving divergence-free is obtained by projecting the velocity onto the divergence-free space after generating the new mesh at the last iterative step. Numerical experiments are presented to demonstrate the effectiveness of the proposed method for solving the incompressible mixture flows.