Comment on “Free surface tension in incompressible smoothed particle hydrodynamics (ISPH)” [Comput. Mech. 2020, 65, 487–502]

We comment on a recent article [Comput. Mech. 2020, 65, 487–502] about surface-tension modeling for free-surface flows with Smoothed Particle Hydrodynamics. The authors motivate part of their work related to a novel principal curvature approximation by the wrong claim that the classical curvature formulation in SPH overestimates the curvature in 3D by a factor of 2. In this note we confirm the correctness of the classical formulation and point out the misconception of the commented article.

Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.

Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications

This Special Issue aimed to provide a forum for the latest advances in hydraulic modeling based on the use of non-linear shallow water equations (NSWEs) and closely related models, as well for their novel applications in practical engineering. NSWEs play a critical role in the modeling and simulation of free surface flows in rivers and coastal areas and can predict tides, storm surge levels and coastline changes from hurricanes and ocean currents. NSWEs also arise in atmospheric flows, debris flows, internal flows and certain hydraulic structures such as open channels and reservoirs. Due to the important scientific value of NSWEs, research on effective and accurate numerical methods for their solutions has attracted great attention in the past two decades. Therefore, in this Special issue, original contributions in the following areas, though not exclusively, have been considered: new conceptual models and applications; flood inundation and routing; open channel flows; irrigation and drainage modeling; numerical simulation in hydraulics; novel numerical methods for shallow water equations and extended models; case studies; and high-performance computing.

Numerical simulation of fluid structure interaction in free-surface flows: the WEC case

In this work we present a numerical framework to carry-out numerical simulations of fluid-structure interaction phenomena in free-surface flows. The framework employs a single-phase method to solve momentum equations and interface advection without solving the gas phase, an immersed boundary method (IBM) to represent the moving solid within the fluid matrix and a fluid structure interaction (FSI) algorithm to couple liquid and solid phases. The method is employed to study the case of a single point wave energy converter (WEC) device, studying its free decay and its response to progressive linear waves.

A Study on Numerical Methodologies in Solving Fluid Flow and Heat Transfer Problems

Numerical methods are described as techniques by which several mathematical problems are formulated, because they may be easily solved with arithmetic operations. These methodologies have a great impact on the current development of finite element theory and other areas. We have given a short study of numerical methodologies applied in fluid flow and heat and mass transfer problems in mechanical engineering which includes finite difference method, Finite element method, Boundary value problems (general), Lattice Boltzmann’s methods, Crank-Nicolsan scheme methods, boundary integral method, Runge-Kutta method, Taylor series method and so on. We have discussed some phenomena taking place in fluids such as surface tension, coning, water scattering, Stokes law, gravity-capillary, and unsteady free-surface flows, swirling, and so on. We have also analyzed boundary value problems on boundary problems, eigenvalue problems and found a numerical way to solve these problems. We have presented different numerical methods applied to different fundamental modeling approaches in heat transfer and the performance of the mechanisms (modes) vary concerning the methods applied. The paper is dedicated to demonstrating how the methods are beneficial in solving real-life heat transfer problems in engineering applications. Results of the parameters like thermal conductivity, energy flux, entropy, temperature, etc. have been compared with the existing methods