Numerical diffusion in Swan

Many numerical methods tend to smooth the computed field. This is illustrated with a Swan model: the bottom is horizontal so that refraction is absent. There is an obstacle with a circular shape in plan. See the picture below. All source terms were switched off.
The incident wave direction was -60°; because there is no refraction the wave direction is -60° everywhere, also in the shadow region. Numerical diffusion transports energy into the shadow region without changing the propagation direction!
There are two numerical schemes for stationary computations: the 1st order scheme (BSBT) and the 2nd order upwind scheme (SORDUP, this is the default propagation scheme). The picture below shows the result of a computation with the BSBT scheme; there are 50 steps in either spatial direction.
The 2nd order scheme performs somewhat better; the picture below shows the computed values of Hs divided by the incoming Hs for the lower boundary of the computational area. Red is the BSBT scheme; green the 2nd order scheme.
The exact solution for this academic case is a discontinuity along a straight line under direction -60° tangent to the circle.
The graph below shows that smaller steps lead to less numerical diffusion; two computations with the 2nd order scheme are compared, one with 50 spatial steps (green), the other with 200 steps in either spatial direction (blue).
The 4th picture shows the spatial distribution resulting from the 2nd order scheme with 200 steps.

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© 2012: Nico Booij