Untitled - Teknik Kelautan / ITB
Untitled - Teknik Kelautan / ITB
Untitled - Teknik Kelautan / ITB
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Application of Finite Volume Cell Center Method with Wet and<br />
Dry Treatment in Hydrodynamic Flow Modeling<br />
Bobby Minola Ginting 1 , Dantje K. Natakusumah 2 , Dhemi Harlan 2 , Herli<br />
Ginting 3<br />
1 Faculty of Engineering, Parahyangan Catholic University<br />
2 Faculty of Civil and Environmental Engineering, Bandung Institute of Technology<br />
3 Faculty of Mathematics and Science, University of North Sumatera<br />
Email: bobbyminola.g@unpar.ac.id, dhemi@si.itb.ac.id<br />
Abstract. Numerical scheme of Finite Volume Cell-Center with Artificial Viscosity<br />
as spatial discretization and Runge Kutta Fourth Order as time stepping is proposed<br />
to solve two dimensional shallow water equations in conservation forms which cover<br />
mass and momentum conservation in both directions. The unstructured curvilinear<br />
mesh is used in domain discretization, while the hybrid formula is applied to Runge<br />
Kutta Fourth Order in time stepping. With this hybrid formula, the artificial term is<br />
only computed once therefore the computational cost can be minimized. The<br />
artificial viscosity is formed by combination of Laplacian and Biharmonic operator<br />
to handle numerical instabilities. The function of Laplacian operator is to stabilize<br />
solution around shock wave phenomenon, and Biharmonic operator is to omit the<br />
wiggle solution. The Biharmonic operator is turned off when hydraulic jump<br />
phenomenon occurred, and conversely, turned on when it disappeared.<br />
Characteristic method is used in boundary condition treatment to determine the<br />
velocity both in x and y directions when water elevation is specified. Wall boundary<br />
condition is treated with normal velocity at the wall is zero condition. Wet and dry<br />
treatment is applied especially for domain with initially dry condition by set a value<br />
limiter for minimum depth. Once the water depth reaches this value, the velocities in<br />
both directions are set to be zero.This program was built and successfully applied for<br />
some hydrodynamic cases. For some initially dry-bed cases, the wet and dry<br />
treatment gives the good results. This method is simple, accurate, efficient and<br />
conservative. It can be concluded that this method shows promise to be applied in<br />
other hydrodynamic cases, especially for complex domain cases.<br />
Keywords: artificial viscosity, finite volume method, hybrid Runge-Kutta, shallow<br />
water equations<br />
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