Flows induced by vertical lifting of a rectangular beam partly immersed into shallow water in a rectangular prismatic channel with a horizontal bottom are studied within the framework of the long-wave approximation. The beam width coincides with the channel width and the lower and upper planes of the beam are parallel to the channel bottom. The lifting process in the general case consists of three stages. At the first stage, the lower surface of the beam is completely located in the liquid, which ascends following the beam under the action of hydrostatic pressure. At the second stage, the edges of the lower surface of the beam leave the water medium, the wetted part of the beam becomes smaller, and the liquid under this part of the beam move upward. At the beginning of the third stage, the beam is separated from water; as a result, liquid lifting that occurred at the second stage leads to the formation of two diverging waves. The liquid flow in the domain adjacent to the lower surface of the beam is calculated analytically, while the liquid flow outside this domain is obtained by means of numerical calculations by the CABARET (compact accurately boundary-adjusting high-resolution technique) scheme, which provides the second order of accuracy on smooth solutions.
LED Lens for Rectangular Beam with Small Divergence Angles
