CFD Mass exchange across a reactive front
 

I have a CFD solver at hand which can deal with 2 phases and so far is able to exchange momentum and energy across the interface, where both phases meet. How this is done is well documented in the following paper "A conservative interface method for compressible flows" by Hu, Khoo and Adams, which publicly available.

In the paper, equation (10) is giving the general idea of how to update the conservative variables in so called "cut-cells", cell's which are cut by the interface (tracked by a level-set method).

In this update routine holds the average energy and momentum exchange. Now I want to extend the code such that it can deal with reactive fronts (like combustion or cavitation).

The arising Riemann problem is now solved by a reactive Riemann solver, which provides next to pressure and velocity across the contact discontinuity, also the mass flow through the reactive front.

So far all good, but now I am having troubles to adjust such that it transports the mass (density) across the front.

I would be very grateful for any thoughts or hints. Thanks in advance!

Paul