An overview is provided of the most common features and problems encountered in the simulation of chemically reacting and/or thermally relaxing fluid flows. The importance of good physical models is demonstrated by a few examples, including instances of catastrophic inaccuracy of simulated results. Two examples of non-equilibrium flow simulations are discussed in some detail: the first involving flows in local chemical equilibrium; the second detailing the growth of biofilms in closed conduits. Current reasearch directions and future endeavors are outlined.

WHERE: TEC 340