Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
A conservative level set method for two phase flow II
Journal of Computational Physics
Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach (Encyclopedia of Mathematics and its Applications)
Distance regularized level set evolution and its application to image segmentation
IEEE Transactions on Image Processing
A conservative level set method suitable for variable-order approximations and unstructured meshes
Journal of Computational Physics
Hi-index | 7.29 |
This paper presents a new conservative level set method for numerical simulation of evolving interfaces. A PDE-constrained optimization problem is formulated and solved in an iterative fashion. The proposed optimal control procedure constrains the level set function to satisfy a conservation law for the corresponding Heaviside function. The target value of the state variable is defined as the solution to the standard level set transport equation. The gradient of the control variable corrects the convective flux in the nonlinear state equation so as to enforce mass conservation while minimizing deviations from the target state. A relaxation term is added when it comes to the design of an iterative solver for the nonlinear system. The potential of the optimization-based approach is illustrated by two numerical examples.