# Solution Initialization and Initial Condition

The geometry of the problem consists only of a rectangular domain. The domain is meshed into a grid with each cell size of 25 microns. The problem needs to be initialized and phase volume needs to be assigned to each cell based on the geometry of the problem. A user defined function was developed to initialize the problem and assign the appropriate phases to each cell in the domain. In order to initiate the oscillations, we introduce ellipticity of 5% in the semicircle diameter. All cells within the semicircle were initialized with volume fraction 1 for zirconium phase. Cells outside the semicircle were assigned volume fraction 1 for the helium phase. The volume fraction of cells at interface was generated using the Geo-Reconstruct scheme.

# Time Step

The time step for transient simulation is selected considering computation time and divergence. The simulation time needs to be long enough to capture 2 complete oscillations cycles to extract frequency of oscillation. Another important aspect to be considered is courant number. Courant number needs to be controlled for the simulation to proceed and not crash it due to divergence. Therefore, in finer mesh, time step should be selected carefully. In this simulation the time step is selected to be 2e-5 s (Figs. 3 and 4).

**Fig. 3 ****Meshed domain with cell size of 25 microns**

**Fig. 4 ****Initial condition with 5% ellipticity**