A parallel second-order unstructured finite volume method for 3D free-surface flows using a σ coordinate

Unstructured Finite-Volume Model of Sediment Scouring Due to Wave Impact on Vertical Seawalls

“…The numerical method used in this paper extends the work presented in Uh Zapata et al [18], where 3D hydrostatic free-surface flows are calculated by using an unstructured finite-volume method of the second order of accuracy in time and space. The present numerical technique incorporates the solution of the Exner equation as developed by Zhang et al [19] to solve flows with mobile beds by using unstructured grids.…”

“…where ω = ∂σ ∂t + u ∂σ ∂x + v ∂σ ∂y + w ∂σ ∂z . Thus, continuity Equation ( 1) can be written for three-dimensional flows in the σ-coordinate system as follows [18]:…”

“…Moreover, there is no time-step restriction for obtaining stable results [22]; however, it results in an implicit formulation. For instance, the intermediate velocity field in (18) is calculated as follows:…”

“…Following [35], this flux limiter value is calculated as min(ψ j ) ≤ ψ e−j ≤ max(ψ j ) for all neighbors j. We refer to the work of the present authors [18,19,36,37] for more details about the UFVM for the complete set of equations.…”

“…In order to simulate sediment scouring because of wave-structure-sediment interactions, in this paper, we extend a finite volume method based on unstructured grids (UFVM) for free-surface flows, initially developed by Uh Zapata et al [18], to include mobile beds as in [19]. The proposed numerical method can be applied for irregular domains in the horizontal, cases with free-surface, and irregular bathymetry using a σ-coordinate system [20].…”