6. Simex Implementation on a DNS Code

This study is dedicated to the implementation, verification, and measurement of execution speed, using the method of manufactured solutions, of a new temporal integration method of the implicit–explicit kind, the Stepwise-IMEX or SIMEX, in the Aeroacoustics, Transition and Turbulence Group’s (GATT) Direct Numerical Simulation (DNS) code. In simulations where \(\mathrm{Ma}\approx 0.1\), or less, SIMEX should be able to reduce the explicit fourth-order Runge–Kutta’s (ERK) execution time, which is currently used. A pilot program was created, in Python, with the Burgers’ 1D equation, using fourth-order compact finite differences, to test from second- to fifth-order SIMEX methods and the mentioned explicit method. Indeed, in these preliminary tests, SIMEX proved to be faster than ERK only with linear Burgers’ equation and only after a certain stiffness level. However, there are indications that some characteristics of the DNS, such as the \(\mathrm{y}\)-axis’ greater refinement, not found in the pilot are favorable to SIMEX. Both the decomposition of the ODE and the iterative method for implicit systems and the chosen tableaus pair have a huge impact on the SIMEX efficiency and will be targeted in next stage of DNS code implementation.