We consider flows caused by a line source in a semi-infinite channel having a sloping bottom. Free-surface solutions with a stagnation point just above the source are computed by an integral equation method which is formulated from the boundary value problem of the flow model. We found that there is an upper bound of Froude number where solutions without waves exist. For small Froude numbers, the approximate solution is determined by power series expansion, and this solution gives a good agreement with the integral equation solution.

MINISIMPOSIUM SESSION: 2. Numerical methods for Partial Differential Equations