Truncation approximations for gravity-capillary free-surface flows

Gravity-capillary free-surface flows past disturbances in a channel of finite depth are considered. These flows are usually assumed to extend from x = -infinity to x = infinity where the x-axis is parallel to the bottom. Many numerical schemes truncate this infinite domain to the interval -B < x < A where A and B are large positive numbers. These truncations introduce inaccuracies, especially when the effect of surface tension is included. In this paper numerical methods are presented which remove these inaccuracies. This is achieved by taking into account the contributions from -infinity to -B and from A to infinity. Explicit computations are presented for a semi-circular obstacle at the bottom of the channel.