Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
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
Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems
SIAM Journal on Scientific Computing
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Applied Numerical Mathematics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
An error indicator monitor function for an r-adaptive finite-element method
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Moving mesh methods with locally varying time steps
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
ACM SIGGRAPH 2005 Papers
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
Adaptive unstructured volume remeshing - I: The method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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We present a coupled moving mesh and level set method for computing incompressible two-phase flow with surface tension. This work extends a recent work of Di et al. [(2005). SIAM J. Sci. Comput. 26, 1036---1056] where a moving mesh strategy was proposed to solve the incompressible Navier---Stokes equations. With the involvement of the level set function and the curvature of the interface, some subtle issues in the moving mesh scheme, in particular the solution interpolation from the old mesh to the new mesh and the choice of monitor functions, require careful considerations. In this work, a simple monitor function is proposed that involves both the level set function and its curvature. The purpose for designing the coupled moving mesh and level set method is to achieve higher resolution for the free surface by using a minimum amount of additional expense. Numerical experiments for air bubbles and water drops are presented to demonstrate the effectiveness of the proposed scheme.