0043-B-Frequenzen von schwappendem Wasser

A fluid with a free surface in a tank may move during an earthquake or other dynamic loading with certain frequencies. There are many possibilities to model this behaviour: From discrete particles, viscous fluids or just based on potential theory.

For the latter case a solution with classical FE-Software might be obtainable using the Lagrangian model of fluids.

The analytical reference solution for this 2D problem has been taken from [1].

A rectangular water tank with a width of L = 5.080 m and a water level of D = 1.905 m (L/D=8/3) is considered.  Plain strain conditions have to be applied.

The assumed material constants of water are: a density of 1000 kg/m³ and a bulk modulus of 2000 N/m². Thus the Poisson ratio is 0.5 while the elasticity and shear modulus will vanish. A numerical solution will require to select material parameters close to these values triggering numerical problems with the so called "incompressibility". (Locking, spurious Escher-Modes etc.)

The boundary conditions are sliding support at the walls. The free surface requires a boundary condition with a stiffness of 10 kN/m² to simulate the pressure change if the water level is changing.