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  • Investigating one-line modelling issues

    Shoreline modelling knowledge transfer project
  • Shoreline modelling knowledge transfer project
  • Shoreline modelling knowledge transfer project
  • Shoreline modelling knowledge transfer project
  • Shoreline modelling knowledge transfer project

Shoreline modelling knowledge transfer project

HR Wallingford and the University of Oxford set up a shorter knowledge transfer project to investigate several issues regarding one-line modelling.

The project was supported with government funding from the Technology Strategy Board. The main objectives of the project were to explore:

Resolution of the one-line beach response equation

In the one-line model the equation for conservation of sand is given by the advection-diffusion equation:

where y is the shoreline position (m), D is the summation of depth of closure and berm height (m), Q is the volume rate of alongshore sediment transport (m3/sec), x is the distance along the shore (m) and t is time (sec).

Time integration

The existing model uses an explicit Euler time integration scheme. This project looked into other explicit schemes: Adams-Bashforth 2nd order (AB2) and Runge-Kutta 4th order (RK4), concluding that Euler and RK4 give the best results in terms of stability and accuracy and therefore discarding the possibility of including AB2 in the model.

Space integration

The numerical scheme used in the model was a forward-time forward-space first order difference method. Other methods were examined in this project: forward-time centre space finite difference (FTCS), upwind differencing (UD), three-level fully implicit scheme (3I) and Crank-Nicholson implicit scheme for the advection equation (CN).

Conclusions

Conformal mapping/strip modelling

Boundary-fitted co-ordinate systems are useful in the numerical solution of two- and three-dimensional field problems and whilst they can be applied to the 1D case the benefit is questionable. Essentially, the method involves mapping any arbitrary-shaped domain onto a rectangle or series of rectangles. This facilitates an exact fit to irregular and curved boundaries, unlike uniform Cartesian grid schemes. The mapping process is based on the numerical solution of a pair of Poisson mapping equations using perimeter co-ordinates as boundary values. The converged solution defines the physical mesh. This mapping process can be applied to combine cross-shore models into a strip model. A working prototype of the strip model was created and plausible results achieved, which require validation.

Authors

Belén Blanco, Ian Townend, Ilektra-Georgia Apostolidou*, Prof Alistair Borthwick* Prof Paul Taylor*, *University of Oxford


Keywords

One-line model; numerical scheme; strip model; knowledge transfer project (KTP)


Completed

2010


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Contact

Giovanni Cuomo

Giovanni Cuomo

Research Director

+44 (0)1491 822 414

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