Iceberg.jl

Performs ice-seawater interface calculations using level set methods. The level set scheme is similar to that described by Chen, et al. (1997). Model state is passed around using a subtype of the ModelState abstract type. Physical constants and parameters are contained in a PhysicalParameters type. See initialize1d() for an example.

Iceberg is new and under development. It requires a recent build of Julia (i.e. 0.3).

Model dimension

Models in one, two, and three dimensions will be supported. Dimension is indicated based on the concrete type of the ModelState type passed to functions. Currently, one-dimensional models are implemented.

Field evolution

Methods to solve the heat equation are contained in heat.jl.

Interface fluxes can be calculated using the front_velocity() function. Level set reinitialization uses a global method described by Chen et al. (1997) and Osher and Fedkiw (2003). In the future, there will be functions to handle level set function evolution with a hyperbolic equation solver.

Validation

The function initialize1d_hill() recreates a scenario easily compared to the analytical solution of Hill (1987), Section 1.3. An instance of this scenario with n=200 is a part of the test suite.

To do

• extend to higher dimensions
• add simple Navier-Stokes field solver for fluid phase

References

Chen, S., B. Merriman, S. Osher and P. Smereka. A simple level set method for solving Stefan problems, 1997. Journal of Computational Physics, 135, 8-29.

Hill, J. M. One-dimensional Stefan Problems: an introduction, 1987. Pitman Monographs and Surveys in Pure and Applied Mathematics, 31. John Wiley and Sons, New York.

Osher, S. and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces, 2003. Applied Mathematical Sciences, 153. Springer-Verlag, New York.