Abstract
A new method for the simulation of run-up using a variable transformation that fixes the shoreline is developed. This method uses equations expressed in the Eulerian description, but requires no artificial conditions at the shoreline. Hence, it may represent the real phenomenon more accurately than existing methods in which artificial conditions or extrapolation are needed. In a one-dimensional example the numerical solution is found to agree with analytic one very well. The method can easily be extended to two dimensions if the shoreline can be transformed into lines that intersect each other at right angles.
