The accurate numerical simulation of physical phenomena is crucial in various scientific and engineering disciplines, and open-source solvers offer flexibility and accessibility to researchers and practitioners. A vital aspect of these solvers is the order of the time stepping scheme employed to evolve the solution over time, as it significantly affects the error of the obtained solutions. This project investigates and verifies the order of different time stepping methods implemented on various solvers. We focused on higher-order methods, which give better accuracy and help reduce the computational costs of obtaining a precise enough solution. To study the order of fluid-structure interaction (FSI) simulations using preCICE, we chose OpenFOAM and Calculix as the studied solvers, which are compatible with this coupling library.
We verified the expected error convergence of second-order methods on both solvers using single-solver simulations and confirmed the correct convergence of first-order methods on FSI simulations. Moreover, we tested higher-order time stepping schemes on FSI simulations and found an incoherent behaviour of the error. We followed by ruling out possible causes of this poor convergence and proposing possible solutions, making this work valuable for future projects aiming to obtain accurate FSI simulations in the preCICE environment.