EPTT 2020

12th Spring School on Transition and Turbulence

SIMEX IMPLEMENTATION 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.EPTT2020.EPT20-0116

 

Abstract

This study is dedicated to the implementation, validation and measuring 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 $ Ma \approx 0.1 $, or less, SIMEX should be able to reduce the explicit $4^{th}$ order Runge-Kutta's (ERK) execution time, which is currently used. A pilot program was created, in Python, with the Burger 1D equation, using $4^{th}$ order compact finite differences, to test from $2^{nd}$ to $5^{th}$ order SIMEX methods and the mentioned explicit method. Indeed, in these preliminary tests, SIMEX did not prove to be faster than ERK, with the best result being a tie. However, there are indications that some characteristics of the DNS, such as the $y$ 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 \textit{tableaus} pair have a huge impact on the SIMEX efficiency and will be targeted in this study's next stage of implementing the method in the DNS.

Keywords

IMEX, SIMEX, Runge-Kutta, Temporal integration.

 

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