# Article

**Summary:**

The work deals with numerical solution of unsteady flows in a 2D channel where one part of the channel wall is changing as a given function of time. The flow is described by the system of Navier-Stokes equations for compressible (laminar) flows. The flow has low velocities (low Mach numbers) and is numerically solved by the finite volume method. Moving grid of quadrilateral cells is considered in the form of conservation laws using ALE (Arbitrary Lagrangian-Eulerian) method.