Numerical Modeling of Wave Run-Up in Shallow Water Flows Using Moving Wet/Dry Interfaces

We present a new class of numerical techniques to
solve shallow water flows over dry areas including run-up. Many
recent investigations on wave run-up in coastal areas are based on
the well-known shallow water equations. Numerical simulations have
also performed to understand the effects of several factors on tsunami
wave impact and run-up in the presence of coastal areas. In all these
simulations the shallow water equations are solved in entire domain
including dry areas and special treatments are used for numerical
solution of singularities at these dry regions. In the present study we
propose a new method to deal with these difficulties by reformulating
the shallow water equations into a new system to be solved only in the
wetted domain. The system is obtained by a change in the coordinates
leading to a set of equations in a moving domain for which the
wet/dry interface is the reconstructed using the wave speed. To solve
the new system we present a finite volume method of Lax-Friedrich
type along with a modified method of characteristics. The method is
well-balanced and accurately resolves dam-break problems over dry
areas.

Authors:

• Alia Alghosoun
• Michael Herty
• Mohammed Seaid

Keywords:

• Run-up waves
• Shallow water equations
• finite volume method
• wet/dry interface
• dam-break problem.

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