Evolution of the free surface of a plane channel during filling with a viscous fluid

The behavior of the free surface of a viscous incompressible fluid is studied in the process of filling of a plane channel inclined to the gravity direction. The problem is numerically solved within the framework of the Navier-Stokes equations under the assumption that the fluid is Newtonian and capillary effects can be neglected. The numerical technique is based on the joint use of the SIMPLE and invariant methods. Two filling regimes are found to exist, namely, that with a steady shape of the free surface without the formation of internal cavities and that with cavity formation in the initial filling stage characterized by spouting behavior of the free boundary.