Characteristic Boundary Conditions for Direct Simulations of Turbulent Counterflow Flames

The direct numerical simulation of counterflow flames using a compressible flow formulation has encountered many numerical difficulties associated with inflow and outflow boundary conditions. In this study, one of the most critical issues is found to be the treatment of the transverse terms in the standard local one-dimensional inviscid (LODI) relations. While this issue applies to the general Navier-Stokes characteristic boundary conditions (NSCBC), the counterflow configuration is one of the first showcases to reveal that the transverse terms can no longer be ignored in the LODI relations. In this study, a modified formulation of LODI including the transverse terms is derived for both inflow and outflow boundary conditions that can prevent spurious pressure and velocity behavior at the boundaries. Test simulations demonstrate that retaining the transverse terms in LODI relations is critical in ensuring correct pressure and velocity fields. In analogy with the pressure damping used in previous studies, an additional transverse term damping is proposed, for which optimal damping coefficients are identified by considering the steady state limit. Applications to nonreacting and reacting counterflow simulations demonstrate the robustness of the improved boundary conditions and their successful implementation