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COBEM 2021
26th International Congress of Mechanical Engineering
IMPLEMENTATION OF THE STEPWISE IMPLICIT-EXPLICIT TIME-STEP METHOD ON A DNS CODE
Submission Author:
Giovanni Braga , SP
Co-Authors:
Giovanni Braga, Marcello Augusto Faraco de Medeiros, Savio Rodrigues
Presenter: Giovanni Braga
doi://10.26678/ABCM.COBEM2021.COB2021-0686
Abstract
This study is dedicated to the implementation, verification via the method of manufactured solutions, and measurement of execution speed of a new temporal integration method of the implicit-explicit kind, the Stepwise-IMEX (SIMEX), in the Aeroacoustics, Transition and Turbulence Group's (GATT) Direct Numerical Simulation (DNS) code. The SIMEX method can extend the maximum stable step size when compared with explicit integration schemes because explicit methods are severely constrained by the CFL condition especially at low Mach number, $ Ma \approx 0.1 $ or less. The SIMEX method can attain a larger step-size by decomposing the compressible Navier-Stokes equation in two parts, one implicit and one explicit, so that only the stiff terms are integrated implicitly. This method's aim is to reduce the execution time demanded by the explicit 4$^{th}$order Runge-Kutta (RK4) which is currently being used by the research group. SIMEX was implementated on the DNS code and three test cases were designed by varying the boundary conditions, then different ESDIRK-ERK \textit{tableaus} pairs ranging from 2$^{nd}$ to 5$^{th}$ order were tested. The iterative method employed for linear systems was the GMRES and for non-linear systems was the Jacobian-free Newton-Krylov method. Both the choice of \textit{tableau} pair and the presence, or not, of boundary conditions, as well as the decomposition, showed an enormous influence on SIMEX's capability to extend the maximum step-size. Regarding the computational efficiency, SIMEX allows one to explore the trade off between the maximum stable step-size and the amount of iterations per step; thus, allowing for an optimal balance between the computational effort placed in each step and the increase in step-size.
Keywords
IMEX, SIMEX, Runge-Kutta, Temporal Integration, Navier-Stokes
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