Interface Curvature Calculations for Rudman Coarse-Fine Conservative Grids

This research extends the standard height function method to include information from a subgrid. This inclusion separates the scheme from traditional height function methods and allows the curvature to respond to subgrid interface perturbations. Height function methods calculate the curvature of a cell by taking information from surrounding cells and building columns. By integrating the volume of fluid within a column, a height is established. Including a subgrid is motivated by the work of Rudman (Int. J. Numer. Meth. Fluids, 1998) who showed using a subgrid allows for both mass and momentum conservation, even in high-density ratio flows.
When a subgrid is used, the standard height function method is not accurate as it fails to capture subgrid interface perturbations. The proposed subgrid height function method captures these perturbations. Several variations of the subgrid height function approach are developed and tested. The variants include a fifth-order method and second-order methods that allow the scale the curvature is computed on to be varied. The methods are tested using an oscillating droplet test case and the robustness of the technique is shown by simulating an atomizing Diesel jet.