We are interested in accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). In our application, the sequence originates from time-stepping within a simulation of an unsteady incompressible flow. To this end, we apply a pressure correction scheme, and we focus on the solution of the Poisson problem for the pressure corrector. Its scalable solution presents the main computational challenge in many applications. The right-hand side of the problem changes in each time step, while the system matrix is constant and symmetric positive definite. The acceleration techniques are studied on a representative problem of flow around a unit sphere. Our baseline approach is based on a parallel solution of each problem in the sequence by nonoverlapping domain decomposition method. The interface problem is solved by PCG with the three-level BDDC preconditioner. We first discuss an appropriate stopping criterion for PCG. Next, two techniques for accelerating the solution are gradually added to the baseline approach: deflation is used within PCG with several approaches to Krylov subspace recycling, and the adaptive selection of the coarse space within the three-level BDDC method is considered. Both algorithmic techniques further reduce the largest eigenvalue of the preconditioned system compared to the baseline approach, hence reducing the condition number and the number of PCG iterations. We present a number of experiments with careful measurements of computational times on a parallel supercomputer. Overall, the combination of the acceleration techniques eventually leads to saving more than 40 % of the computational time. The presentation is based on our recent paper [M. Hanek, J. Papež, and J. Šístek. Speeding up an unsteady flow simulation by adaptive BDDC and Krylov subspace recycling. Computer Methods in Applied Mechanics and Engineering, 452:118788, 2026].