The impacts of the ALE and hydrostatic-pressure approaches on the energy budget of unsteady free-surface flows

Abstract

This paper focuses on the energy budget in the calculation of unsteady free-surface flows on moving grids with and without using the 'arbitrary Lagrangian-Eulerian' (ALE) formulation or hydrostatic-pressure assumption. The numerical tool is an in-house general-purpose solver for the unsteady, incompressible and homogeneous Navier-Stokes equations in a Cartesian domain. An explicit fractionalstep method and co-located finite-volume method are used for the second-order accurate integrations in time and space. The test cases are nonlinear and linear irrotational standing waves, which allow to characterise the impacts of an ALE or Eulerian formulation with moving grids by comparison with the anticipated energy conservation. The study is also extended to viscous waves for varying waveheight-to-water-depth and basin aspect ratios. The Eulerian viewpoint produces marked overdamping as early as in the first wave period for the range of relative wave heights g 0 /h > 0.01, where g 0 is the wave semi-amplitude and h is the undisturbed water depth. The hydrostatic calculations misrepresent the evolution of the potential and kinetic energies for h/L > 0.1, where L is the basin length, with spurious modes arising from different initial conditions.

Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows

“…(1) and (2) are resolved using the finite-volume numerical code PANORMUS (PArallel Numerical Open-souRce Model for Unsteady flow Simulations) (Napoli, 2011), which is second-order accurate both in time and space. The numerical model uses the explicit Adams-Bashforth method for the time advancement of the solution, while the fractional-step technique is used to overcome the pressure-velocity decoupling, in conjunction with the multigrid accelerator V-cycle (further details on the numerical procedure can be found in Lipari and Napoli (2008)). The numerical model was extensively and favorably validated over a wide range of cases (Cioffi et al, 2005, Jozsa et al, 2007, De Marchis et al, 2010, 2012.…”

Wind- and tide-induced currents in the Stagnone lagoon (Sicily)

“…The parameter α controlling the node clustering is locally tuned to obtain a vertical resolution not higher than 0.05 m in the top cell (resulting in a null value of the parameter and an uniform vertical discretization where the water depth is lower than 0.05 n m). Details on the numerical discretization and extensive validation of PANORMUS model against laboratory and field experiments in several different conditions can be found in Cioffi et al [6], De Marchis and Napoli [7], Lipari and Napoli [16] and Napoli et al [20].…”

An improved immersed boundary method for curvilinear grids

“…In particular both the lift and the drag coefficients fall out of the range of values given in Eqs. (19) and (20). In order to further confirm that the use of curvilinear grids gives more flexibility and consequently allows obtaining more accurate results with respect to Cartesian ones, in Fig.…”

“…14 the lower and upper bounds of the coefficients are also plotted (see Eqs. (19) and (20)) as obtained using the data of the research groups involved in the aforementioned DFG Priority Research Program. The coefficients obtained in our computations fall within the prescribed range of values in cases C0 and C1, using both Cartesian and curvilinear grids.…”

“…Continuous lines with circles: Cartesian grids. The dashed horizontal lines give the range of values of Eqs (19). and(20).…”