Convergence performance of DPLR implicit algorithm for solving thermochemical nonequilibrium flow

Slow convergence is a major challenge in the numerical simulation of thermochemical non-equilibrium flows. This study presents a comprehensive comparative analysis of the convergence performance of the data parallel line relaxation (DPLR) implicit algorithm under high-speed reentry conditions by simulating thermochemical nonequilibrium flow over a 10 mm sphere and the Apollo capsule. The results demonstrate that DPLR exhibits excellent convergence characteristics and can reach steady state within a few thousand iterations across a wide range of flow conditions. These conditions encompass freestream densities spanning four orders of magnitude, velocities from 4 to 10 km/s, and chemical models ranging from 5 to 11 species, along with both single- and two- temperature thermodynamic equilibrium and nonequilibrium models, as well as various thermodynamic properties, transport coefficients, and chemical kinetics models. Furthermore, the implementation of implicit boundary conditions is identified as a critical factor for achieving fast convergence of DPLR in thermochemical nonequilibrium simulations. Overall, the convergence performance of the DPLR algorithm is demonstrated to be superior to that of the lower-upper symmetric Gauss-Seidel (LU-SGS) method for both simple forebody and complex afterbody flows. Under the present computational conditions, the convergence times of DPLR are approximately 3.4% and 8% of those of the LU-SGS method, respectively. This research provides valuable references for the engineering applications of the DPLR implicit algorithm.