[RCBlast]

Hello everyone,
I've written a 1D CFD code based on the nondimensional conservation form described in Chapter 7 of Anderson's "Computational Fluid Dynamics" book. The code works great so far! I'm trying to introduce steady heating to account for afterburn in oxy-fuel detonation in a semi-empirical manner.
I am trying to increase the temperature of n nodes uniformly over a specified period of afterburn time. I am doing this by stepping into the simulation at each time step and increasing the temperature at the previous time step by a small value for each of the n afterburn nodes. This changes the primitive variable U3, but does not change U1 or U2.
The issue that I'm having is that after about 200 time steps, the temperature in the nodes I'm trying to heat has "blown-up" and the solution eventually breaks down and fails. The total increase in temperature I'm trying to induce is relatively small, but it seems that the temperature accumulates and is an order of magnitude more than it should be.
I feel like I'm violating the physics of the problem, hence why the solution fails. Do you experts have any suggestions for how to properly incorporate steady heating? I am share more details of the code as requested.
Thanks!