In computations of unsteady flow problems by the arbitrary Lagrangian–Eulerian (ALE) method, the introduction of the grid velocity in the transport terms of the governing equations is not a sufficient condition for conservativeness if topology changes in the dynamic mesh are present and the number of mesh cells changes. We discuss an extension to second-order time differencing schemes (Implicit Euler and Crank–Nicolson) in the finite volume framework, to achieve second-order time-accuracy of the solution. Numerical experiments are given to illustrate the effectiveness of the presented method.