Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Journal of Scientific Computing
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
Journal of Computational Physics
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations
Journal of Scientific Computing
Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems
Journal of Scientific Computing
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows
Journal of Scientific Computing
Mesh Update Techniques for Free-Surface Flow Solvers Using Spectral Element Method
Journal of Scientific Computing
Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators
Computers & Mathematics with Applications
Discontinuous Galerkin spectral element approximations on moving meshes
Journal of Computational Physics
High order numerical approximation of minimal surfaces
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
We present a new method for tracking an interface immersed in a given velocity field which is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian-Eulerian (ALE) framework. The new method has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to automatically achieve a good distribution of the grid points along the interface. In order to achieve these goals, information from a pure Lagrangian approach is combined with information from an ALE approach. Our implementation relies on the solution of several pure convection problems along the interface in order to obtain the relevant information. The new method offers flexibility in terms of how an ''optimal'' point distribution should be defined. We have proposed several model problems, each with a prescribed time-dependent velocity field and starting with a prescribed interface; these problems should be useful in order to validate the accuracy of interface-tracking algorithms, e.g., as part of an ALE solver for free surface flows. We have been able to verify first, second, and third order temporal accuracy for the new method by solving these two-dimensional model problems.