A comparative analysis of explicit, IMEX and implicit strong stability preserving Runge-Kutta schemes

Convergence towards High-Speed Steady States Using High-Order Accurate Shock-Capturing Schemes

“…Secondand third-order accurate implicit-explicit (IMEX) RK schemes also exist [54], but only the explicit part is SSP. However, there is strong evidence that the nonlinear upper bound imposed on the time steps of implicit and IMEX SSP-RK schemes renders them inefficient when compared to their explicit counterparts [55]. Hence, they are not used in 3D4S for time-accurate simulations.…”

“…No slip and isothermal walls are considered with T w = T ∞ = 216.67. Figure 6 presents a sketch of the analytic grid used in these simulations, and a complete discussion of grid generation can be found elsewhere [6]. The density wall-normal profile at the corner (left) and density-maximum residue convergence in time (right) obtained for three different free stream Reynolds numbers, namely Re ∞ = 2 × 10 3 (top), 5 × 10 3 (middle), and 10 × 10 3 (bottom), are show in Figure 7 for the isotherm wall under different grid sizes.…”

“…This system is obtained here by applying finite-difference schemes under a generalized coordinate framework to the spatial operators of the model. The code developed to run all the simulations presented here is called 3D4S [6,7]. It stands for one-, two-, and threedimensional structured steady-state solvers and uses the C++ programming language [8].…”