 
Summary: Wave Reflection over Slowly Varying Bathymetry modeled
by Effective Boundary Conditions
W. Kristina, E. van Groesen, O. Bokhove
Department of Applied Mathematics, Universiteit Twente, The Netherlands
Linear Shallow Water Equations
WKB Approximation Effective Boundary Condition over
Slowly Varying Bathymetry
Introduction
In tsunami simulations, the waveheight near the shore is the most important
aspect scientists would like to calculate correctly. Unfortunately, the presentday
simulation tools still cannot calculate the waveheight near the shore accurately
enough. One source of inaccuracy is the interaction of the incoming waves with
reflected waves from the coast. Besides, computing the details of runup and run
down of waves on the shore is computationally very demanding and expensive
since closer to the shore a finer computational resolution will be needed.
Moreover, the modeling of the physical processes is bound to be rather
rudimentary because many aspects of tsunami propagation, e.g. nonlinearity,
dispersion, friction, etc. have to be considered.
Most of the tsunami simulations nowadays will use a fixed wall as boundary
condition at the shore to simplify the problem. But this will cause inaccuracies in
