Verification of variable-density flow solvers using manufactured solutions

The method of manufactured solutions (MMS) is used to verify the convergence properties of a low-Mach number, variable-density flow code. Three MMS problems relevant to combustion applications are presented and tested on a variety of structured and unstructured grids. Several issues are investigated, including the use of tabulated state properties (i.e., density) and the effect of sub-iterations in the time-advancement method. The MMS implementations provide a quantitative framework to evaluate the impact of these practices on the code’s convergence and order-of-accuracy. Simulation results show that linear interpolation of the equation-of-state causes numerical fluctuations that impede convergence and reduce accuracy. Likewise, the sub-iterative time-advancement scheme requires a significant number of outer iterations to subdue splitting errors in highly nonlinear combustion problems. These findings highlight the importance of careful code and solution verification in the simulation of variable-density flows.