title: Numerical studies of 2D free surface waves with fixed bottom
abstract: The motion of surface waves under the effect of bottom is a very interesting and challenging phenomenon in the nature. we use boundary integral method to compute and analyze this problem. In the linear analysis, the linearized equations have bounded error increase under some compatible conditions. This contributes to the cancellation of instable Kelvin-Helmholtz terms. Under the effect of bottom, the existence of equations is hard to determine, but given some limitations it proves true. These limitations are that the swing of interfaces should be small enough, and the distance between surface and bottom should be large enough. In order to maintain the stability of computation, some compatible relationship must be satisfied. In the numerical examples, the simulation of standing waves and breaking waves are calculated. And in the case of shallow bottom, we found that the behavior of waves are rather singular
keyphrases: numerical studies 2D free surface waves boundary integral method linear analysis linearized equations instable Kelvin-Helmholtz terms