Elsevier

Coastal Engineering

Volume 164, March 2021, 103799
Coastal Engineering

Wave and structure interaction using multi-domain couplings for Navier-Stokes solvers in OpenFOAM®. Part I: Implementation and validation

https://doi.org/10.1016/j.coastaleng.2020.103799Get rights and content

Highlights

  • One-way and two-way 2D-3D multi-domain couplings have been developed for Navier-Stokes models.

  • A wide range of wave conditions were successfully transferred, including infragravity waves.

  • A high field smoothness was shown through the interfaces.

  • The 2D-3D approach has proven to be robust and stable.

  • The methodology significantly reduces the computational time.

Abstract

This paper and its companion (Di Paolo et al., 2020b) present near-far field coupling schemes of Navier-Stokes (NS) equations for high-fidelity numerical modelling of wave generation, transformation and interaction with structures. The computational domain is subdivided into near and far field zones (2D and 3D subdomains, respectively) in which the NS equations are solved adopting the Finite Volume Method. The couplings can be made through the one-way or two-way exchange of flow information, thus providing a complete tool for studying one or bi-directional processes in which the three-dimensional flow is expected to be confined in the near field. The global coupled system, which is built on the OpenFOAM® platform, is based on a multi-domain approach in which the sub-domains (i.e., 2D and 3D meshes) are built independently.

In Part I, the coupling methodologies have been validated against full 3D models taking into account wave propagation under different conditions with excellent results and high efficiency.

Part 2 (Di Paolo et al., 2020b) involves the validation and application of the proposed methodologies to complex wave-structure interaction studies.

Introduction

During the past decades, the use of Computational Fluid Dynamics (CFD) based models has experienced an important increase in coastal and offshore engineering as they are highly accurate to study wave transformation, wave-breaking and fluid-structure interaction processes. Because the computational cost is tremendously high when using a single 3D model, its application is unfeasible for large domains (Vandebeek et al. (2018)). Therefore, traditionally the application of CFD modelling has been limited to small scale domains forced by appropriate boundary conditions. However, the main drawback of this approach is that it does not allow to properly include wave propagation and shoaling. Thus, in recent years, a considerable research effort has been made on developing near-far field coupled models that were able to deal with the above issue in an efficient way (e.g. Altomare et al. (2014); Vandebeek et al. (2018)).

Coupled models for water wave applications have been generally classified based on the physics involved, i.e. single or multi physics, and, depending on the linkage between solvers, as “one-way” or “two-way”. One-way couplings, also known as “weak” or “one-directional” couplings allow information to pass in one direction, while “two-way” coupling, also known as “strong” or “bi-directional” couplings allow information to be exchanged in two directions. “One-way” couplings are used when the processes involved can be assumed to be one-directional whereas “two-way” couplings are required when the bi-directionality cannot be neglected.

In the following, some previous works, considered key for the development of the current research, are reviewed and ranked from computationally cheaper or “lower” to expensive or “higher” models. Here we focused on the coupled models (considering single or multi physics) addressing the hydrodynamics of water waves. Considering the governing equations solved four categories can be identified, i.e., fully non-linear potential flow (FNPF), non-linear shallow water (NLSW), Boussinesq-type (BT) and Navier-Stokes based (CFD) models. The coupling techniques among the above, in “one-way” or “two-way” modes, are reviewed in the following.

Several weak (“one-way”) coupled models (Lagrangian or Eulerian) have been developed by the scientific community. For example, fully non-linear potential solvers (FNPF) have been coupled with RANS-VOF and Smoothed Particle Hydrodynamics (SPH) models (e.g. Hildebrandt et al. (2013); Fourtakas et al. (2018), respectively). Hildebrandt et al. (2013) simulated wave impact on a tripod structure by implementing a one-way coupling as no reflection of the impact waves was expected. Fourtakas et al. (2018) validated the FNPF-SPH coupling for the propagation of two sinusoidal waves but the method was not tested for wave interaction, neither with coastal nor with offshore structures. The one-directional coupling methodology has been applied to link BEM (Boundary Element Method) potential flow codes and VOF solvers (e.g. Lachaume et al. (2003); Biausser et al. (2004)). In particular, Lachaume et al. (2003) modelled breaking and post-breaking waves on slopes by coupling BEM and RANS-VOF software. Zhang et al. (2013) coupled Navier-Stokes (NS) with Potential Flow (PF) solvers for near and far field wave propagation, respectively, describing weak and strong coupling implementation. Duz et al. (2016) implemented a coupling between OceanWave3D (FNPF) and ReFRESCO (RANS-VOF) models. They analysed the capabilities of two FNPFs and SWASH (NLSW) models and stated that none of them is superior to the other for wave propagation studies, thus the computationally cheapest one (OceanWave3D) was coupled with the RANS-VOF solver. Paulsen et al. (2014) also presented a one-way coupling between the potential flow solver OceanWave3D and a RANS-VOF solver in OpenFOAM environment. The one-way coupled method was validated for wave interaction with surface piercing structures, also considering complex hydrodynamics (i.e. multi-directional irregular waves on a sloping bed). Another interesting work was proposed by Vukčević et al. (2016). They implemented a decomposition method in which a generic field is decomposed into an incident wave forcing component and a perturbation component. The incident wave forcing component was obtained from a potential flow model, while the perturbation component was adjusted in order to satisfy the conservation equations in the NS based model. The method implemented by Vukčević et al. (2016) has been recently reproposed by Li et al. (2020). The main differences of their work lie in the simplification of continuity and momentum equations, the use of VOF technique instead of the Decomposed Level-Set approach and the interpolation method used to transfer information from the potential solver to the NS model. The latter showed that the Decomposed Level-Set approach has no advantages against the VOF method.

NLSW codes have been coupled with RANS/VOF solvers (Vandebeek et al. (2018)). Vandebeek et al. (2018) validated a weak coupling between the non-hydrostatic NLSW model (SWASH) and the RANS-VOF (OpenFOAM). However, the coupling was only tested for the propagation of a first order linear wave on a flat bottom. Neither wave structure interaction (WSI) nor coupling effects were analysed. The results of regular wave propagation showed a small damping in the free surface elevation far from the coupling zone. SWASH has also been “one-way” coupled with SPH as proposed by Altomare et al. (2014) for coastal engineering problems. They motivated their work based on the fact that SWASH is able to propagate waves with comparable accuracy to BT models while the full SPH simulation could damp waves if applied to long distances. However SWASH may lead to computation stability problems when applied to rapidly changing bathymetry or structures (Altomare et al. (2014)).

Boussinesq-type models (BT) have found favour over the past decades as they are a good compromise between physical adequacy and computational demand, thus becoming probably the best alternative to CFD codes (Brocchini (2013)). BT models have been coupled with Eulerian and Lagrangian CFD codes. Kassiotis et al. (2011)) proposed the coupling between SPH and BT models. They concluded that the weak coupling was only accurate when waves did not reflect from SPH to the BT domain (Kassiotis et al. (2011)). However, a discontinuous and non-smooth velocity profile appeared at the interface when passing information from an empty flume in the BT domain to the SPH region, before reflection took place (see Fig. 4 of Kassiotis et al. (2011)).

Some works can be found regarding CFD-CFD couplings in one-way mode. Kumar et al. (2015) coupled, breaking waves on 3D structures SPH-FVM solvers within the OpenFOAM® environment. They used the FVM solver from OpenFOAM to simulate a large domain while the application of SPH was limited to a small region on free surfaces and near deformable boundaries. El Safti et al. (2014) coupled 2D with 3D RANS-VOF simulations in OpenFOAM® by forcing the 3D model by means of post-processed sensor data in the 2D simulation. In the work of El Safti et al. (2014) neither active wave absorption (AWA) nor a fully coupled multi-region scheme were considered, so that although a 2D-3D coupling was developed the domains were increased at the interfaces as the relaxation method (Jacobsen et al. (2012)) was used (two relaxation zones). Furthermore, in the work presented in El Safti et al. (2014), Large Eddy simulation was performed which considerably increased the computational time, making the methodology unfeasible for the study of large domains. In addition, no two-way coupled scheme was applied to the 2D-3D coupling.

Many past works have also focused on “two-way” methodologies to analyse those cases where the flows travel through the distinct domains in different directions. Verbrugghe et al. (2018) and Verbrugghe et al. (2019) proposed strong FNPF-SPH couplings. In Verbrugghe et al. (2018) the communication between models was implemented using OpenMPI, that was managed through a main script coded in Python language. Although, different non-linear waves were propagated and some simulation for WSI were performed, neither shallow foreshores (coastal applications) nor three-dimensional local effects were considered. Recently, Kemper et al. (2019) implemented a new nested two-way coupling between FNPF and RANS-VOF models to study hydrodynamics around WEC arrays. The coupled model presented by Kemper et al. (2019) was successfully validated against experimental and analytical solutions. However, the authors stated as the main limitation of the approach that the model was not able to run in parallel and pointed out the need for filtering the RANS-VOF free surface signal before using it as a boundary condition for the FNPF solver. Sriram et al. (2014) carried out a unique 2D-2D strong-coupling between the Improved Meshless Local Petrov Galerkin method (IMLPG_R) based on NS equations and a finite element method model (FEM) based on FNPF. Some research has also addressed the coupling of BEM-based models with potential models and Level-Set (LS) or VOF solvers (e.g. Colicchio et al. (2006) and Kim et al. (2010), Guo et al. (2012), respectively). Another interesting coupling between FNPF and RANS models was implemented in OpenFOAM by Lu et al. (2017). They used an overlapping domain for developing a near-far field method for WSI including overset mesh capabilities in the RANS solver. Janssen et al. (2010) formulated a strongly coupled model linking FNPF and Lattice-Boltzmann based solvers in order to study wave breaking and wave structure interaction. Mintgen and Manhart (2018) implemented a bi-directional coupling of the 2D shallow water equations (SWE) and the 3D RANS-VOF model. An innovative multi-region approach in OpenFOAM was used to combine both methods, and the communication between them was achieved via boundary conditions following a Dirichlet-Neumann approach (see Table 1, Table 2 of Mintgen and Manhart (2018)). However, this work is of limited applications in coastal engineering as only shallow water flows can be studied in the far field. A BT-SPH two-way coupling was presented by Narayanaswamy (2008), in which FUNWAVE (BT) and SPHysics (SPH) were linked in order to study wave propagation. Sitanggang (2008), Sitanggang and Lynett (2010) and Sitanggang et al. (2007) presented a linkage between a 1D horizontal BT solver and a 2DV RANS-VOF model for large-scale simulation. They implemented a nested technique to couple both models. Validation was presented for wave propagation, wave overtopping, wave interaction with permeable structures and large-scale tsunami wave simulation. Despite of very good results obtained by these authors, the coupled methodology was limited to study 2D problems as the RANS-VOF model did not include 3D solutions of the NS equations.

Finally, one of the most interesting two-way couplings was proposed by Ferrer et al. (2016), in which a multi-region compressible-incompressible scheme (multi-physics) was implemented in the OpenFOAM® framework to deal with aerated impact in numerical wave tanks. It is worth noticing that the multi-region approach means that different finite volume meshes are built, each one containing a specific solver, and are solved in a unique global simulation. On the other hand, in a “partitioned approach” different pieces of software (solvers) are independently used, and the interface among them is in charge of the message passing information (MPI etc.), as shown in Verbrugghe et al. (2018). Table 1 summarises the references above and also includes other interesting works.

In this work, new coupling methodologies are developed in order to study wave propagation, breaking and interaction with structures using CFD based models only. Coupling 2D and 3D CFD solvers can represent an extremely accurate and efficient approach as it is a compromise between the computational cheaper couplings (e.g. NLSW-CFD or BT-CFD) and the extremely expensive full 3D simulations. A key aspect of the proposed research is that by using the 2D-3D RANS-RANS approach, the flow variables of the 3D model are continuously enriched by means of highly resolved hydrodynamics from the 2D solver, thus increasing the accuracy of the near-far field hydrodynamic modelling.

Although the use of BT or non-hydrostatic NLSW codes for wave transformation has been common practise, the application of CFD allows to reduce uncertainties in hydrodynamic modelling as the full set of NS equations is solved. Moreover, the performance of heterogeneous couplings (different models, e.g. NLSW-CFD or BT-CFD) has not been analysed in depth considering an extended range of wave forcings, local conditions (i.e. shallow, deep and intermediate waters) and the influence of depth varying flow at the coupling zone. Difficulties may also arise in order to avoid wave damping and distortion when matching “heterogeneous models” at the coupling zone. Such as, in BT-CFD couplings the BT model can only provide velocity and free surface at a reference depth (Narayanaswamy (2008)). This leads to a loss of accuracy especially when the velocity profile varies significantly along the water depth. Moreover, an overlapping zone is generally needed to develop BT-CFD couplings (Narayanaswamy (2008); Sitanggang and Lynett (2010); Kassiotis et al. (2011)). For complex cases, where the 3D domain typically governs the computational time, the BT-CFD model might be more expensive than a 2D-3D CFD-CFD one.

The methodology developed in the present work aims at providing an extremely accurate tool to model numerically those processes in which three dimensional flows are dominating in the near-field. The computational speed-up that can be achieved with a 2D-3D approach is high compared to the fully 3D modelling. In fact, the 2D-3D based coupling is further justified by the fact than the CPU time is generally governed by the 3D model whereas the 2D approach is computationally cheaper. Moreover, the accuracy in wave generation is much higher when using a CFD model as the spatial variability of the wave profiles can be estimated with great precision. As an example, the mimicking of wave-maker devices is a unique asset of CFD solvers compared to the computationally cheaper codes. Finally, an additional advantage of a RANS-RANS coupled approach is that it allows forcing the position of the coupling zone closer to the breaking point, while the application of other models (e.g. BT or NLSW) restricts the definition of the coupling boundary to far from the breaking conditions.

The coupled models presented in the current work are intended: (i) to accurately simulate first and second order waves, the propagation and shoaling processes from far to near field, also considering the interaction with complex bathymetry or submerged structures, (ii) to provide a complementary tool of one-way and two-way couplings to be used depending on flow characteristics, (iii) to simulate wave transformation over larger domains with a reduced computational time and (iv) to develop an easy-to-use and parallelised multi-domain scheme in which each computational mesh is built independently. The coupled models presented are capable of simulating large domains in standard desktop computer in a very efficient way, increasing the range of application and the use of CFD to real cases.

The paper is organised as follows. Section 2 describes the coupling methodology developed for the one-way and two-way approaches. Then, Section 3 illustrates the validation of the methodology. Section 4 discusses the advantages of the coupled models and concluding remarks close the paper.

Section snippets

The coupling methodology

The present study is based on the decomposition of a global domain into separated 2D and 3D domains that act as partitioned sub-domains in which different local meshes can be defined (e.g. Mintgen and Manhart (2018)). This approach makes it possible to build regions with different spatial dimensions (i.e. 2D/3D), which is a major advantage over a single global mesh approach (e.g. Ferrer et al. (2016)). The exchange of information between 2D and 3D domains can be performed by means of one-way or

Validation and analysis of the coupling methodologies

Several validation cases have been developed, such as, waves propagating on a horizontal bottom in an empty numerical domain. These benchmark cases are key to verify the capability of the coupling schemes to reproduce wave patterns with very high accuracy and without introducing disturbances at the coupling boundaries. Because the proposed models are intended to be used when a high accuracy in simulating the hydrodynamics is needed, non-linear waves as well as a second order wave generation

Discussion

One of the most significant findings emerging from this study is that wave generation, transformation and interaction with structures in large domains can be efficiently simulated with CFD models using 2D-3D couplings, resulting in a very high accuracy and affordable computational cost and avoiding the assumption of lower models (e.g. potential models). It is worth to notice that a two-way coupling is also introduced for the first time to 2D-3D RANS-RANS coupled models compared to similar

Concluding remarks

Modelling coastal processes using CFD software is a challenging task, mainly due to its extremely expensive computational time when simulating large three dimensional domains. To reduce the computational time and to avoid potential flow assumptions, 2D-3D weak and strong RANS-RANS couplings were proposed in this paper to form the basis for an efficient high fidelity coupling methodology for first and second order hydrodynamics.

The first conclusion is that, compared to 3D models, the one-way and

CRediT authorship contribution statement

Benedetto Di Paolo: Conceptualization, Conception and design of study, Investigation, Formal analysis, Writing - original draft, Drafting the manuscript, Revising the manuscript critically for important intellectual content. Javier L. Lara: Conceptualization, Conception and design of study, Investigation, Formal analysis, Writing - original draft, Drafting the manuscript, Revising the manuscript critically for important intellectual content. Gabriel Barajas: Conceptualization, Conception and

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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