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Flux-based level set method and its applications

Friday, March 18, 10AM – 11:30AM
POB 6.304

Peter Frolkovic

The level set methods are used for numerical simulation of problems involving moving interfaces or boundaries. The idea is to represent the interface implicitly with no moving grid nodes to track the dynamic position of interface. In this talk we introduce several applications of so called flux-based level set method. This method follows the principles of high-resolution finite volume method applied to nonlinear advection-diffusion equation in non-divergent form.

The advantage of flux-based level set method is its simple form even for unstructured 2D/3D grids having second order accuracy for examples with smooth solutions. Although the method is explicit in time for the advection part with usual CFL restriction, a simple extension of the method having significantly relaxed restriction on the CFL number is available.

The flux-based level set method has been applied for several different problems like the advection dominated contaminant transport, the advection of interface, the time dependent eikonal equation and the extrapolation along characteristics. In these problems some related partial differential equations have to be solved on the domain with implicitly given moving boundary. To extend standard discretization techniques for these kinds of problems we use the ideas of immersed interface methods. Examples of the flux-based level set method for applications like two-phase flow, fire spreading and groundwater flow with moving water table using all described ideas will be presented in this talk.

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