A Numerical Model for Aerated-Water Wave Impact on a Coastal Structure

Validation of robust SPH schemes for fully compressible multiphase flows

“…They are both Riemann problems and admit exact solutions, which are found via a procedure described in [15]. In addition to the analytical solution, a reference solution is obtained with…”

A compressible two-phase flow model for pressure oscillations in air entrapments following green water impact events on ships

“…Wemmenhove [35], and also Plumerault [27], neglect the term (∇u) T in the viscous term, as is common to do. Wemmenhove et al [36] do include the term in their mathematical description, but do not evaluate its effect.…”

“…The boxed terms are added when the term (∇u) T is not neglected. As the viscosity is variable around the interface and ∇ • u = 0 for air, the term ∇ • (μ(∇u + ∇u T )) is not equal to ∇ • (μ∇u) as assumed by others [27,35].…”

“…These are found by linear interpolation between the corner point viscosity values μ n,w and μ n,e , μ s,w and μ s,e , respectively. These corner point values between adjacent cell centers are found by harmonic averaging [27]. For computing the local average viscosity at a pressure point, Eq.…”

“…During green water events involving a complex configuration of the free surface, air and water interact in a way that can lead to entrained air and entrapment of large air pockets. By entrapping an air pocket between the water and the structure, the pocket can have a cushioning effect on the peak pressure on the one hand [5,27]. On the other hand, it can give an increase of the acting force on the structure during a wave impact [5,26] and the pressure oscillations in the air pocket can increase pressure levels on the structure being impacted [27] as well as induce resonant fluid-structure interaction [3].…”