A Domain-Dividing RBF-Based Level-Set Method for a Moving Interface

摘要

In a conventional Level Set Method, the renewal of a signed distancefunction usually relies on a re-initialization process. In this paper, analternative method is proposed to capture locally moving interfaces byintroducing Radial Basis Functions (RBF). This approach provides anaccurate and conservative representation of both the implicit functionand the interfaces. The signed distance function is rebuilt using basicfunctions and weighting coefficients. Its deformation is considered asan updating procedure of the RBF interpolators, transforming themathematical description of the problem from a partial differentialequation (PDE) into one using an ordinary differential equation (ODE).A re-initialization process is no longer needed hence avoiding largenumerical errors. Numerical examples show that the proposed domaindividingRBF-Based Level Set Method improves both the accuracy andmass conservation procedure to capture movement and deformation ofinterfaces, more specifically, of free surfaces.