Two-phase Flow Solver Research Articles

A multi-directional advection based moment of fluid method for phase change problems

A multi-directional face-flux based Moment of Fluid (MoF) advection method is developed to simulate two-phase flows with and without phase change. The material volume and centroid are advected in a face-flux based approach which guarantees the conservation of the advected quantities. The face-flux based advection avoids material overlap and void formation between the advected material volumes. The centroid advection of a material volume is computed by advecting the individual centroids of smaller subvolumes. Hence, the proposed procedure reduces the centroid advection error which is proportional to the size of the material volume. Also, the multi-directional advection enables two-phase simulations over unstructured meshes. A two-phase flow solver with the proposed method is used successfully to study film boiling and condensation phenomena.

Investigations on the jets and shock waves of a cavitation bubble collapsing between a wall and a particle

The simultaneous presence of particles and cavitation bubbles has a deleterious effect on the performance and safety of hydraulic machinery through the generation of jets and shock waves. In the present paper, the mechanisms responsible for the generation and the evolution of jets and shock waves from a collapsing cavitation bubble situated between a spherical particle and a wall are simulated using a compressible two-phase flow solver. Specifically, the effects of bubble position on jet and shock wave behavior are qualitatively analyzed. The simulations and experiments reveal three typical cases of jet behavior: a jet toward the wall, double jets, and a jet toward the particle. Needle jets and shock waves are commonly generated by collisions of the bubble interface. In some cases, needle jets are associated with a high impact velocity. It is found that the smaller the distance between the particle and the wall, the higher the pressure generated by the jets and the shock waves on the wall.

Effects of cathode gas diffusion layer porosity and contact angle distributions along through-plane direction on the performance of polymer electrolyte membrane fuel cell

In the present work, a numerical model for polymer electrolyte membrane fuel cell (PEMFC) has been employed to investigate the effects of porosity and contact angle distributions of the porous layer on the performance of PEMFC. The three-dimensional, two-phase, and non-isothermal flow solver considers heat transfer, electrochemical reaction, and liquid water saturation. Various cases with different cathode gas diffusion layer (GDL) porosities are performed. The results showed that a better performance is achieved when the GDL porosity is increased because of the reduced mass transport resistance of oxygen. The effects of the porosity distributions on the PEMFC performance were examined by comparing the predictions from the cases with non-uniform porosity and uniform porosity in the cathode GDL. It was shown that the current density of the cases with non-uniform porosity is higher than that of the uniform porosity case when the operation voltage is low. This is due to the fact that non-uniform porosity distributions in the cathode GDL enhance the reactant transport. When the operation voltage is high, the current densities of the cases with non-uniform porosity and uniform porosity are almost the same. Moreover, the influence of contact angle distributions in cathode GDL was explored. Various cases with gradient-decreasing, gradient-increasing, and uniform constant contact angles from GDL/channel interface to GDL/catalyst layer interface were studied. It was found that the case with gradient-increasing contact angle has a better performance due to the larger capillary pressure difference to remove more water. The poor performance of the case with gradient-decreasing contact angle is related to the phenomenon of flooding in the catalyst layer.

A compressible solver for two phase-flows with phase change for bubble cavitation

The present work describes the development of a novel fully compressible solver for two-phase flows with liquid-vapour phase change. Phase change phenomena in compressible two-phase flows are driving mechanisms for a multitude of phenomena including cavitation, droplet evaporation in acoustic fields, phase change in closed environments. Those are fundamental for a large number of technological applications including combustion chambers, propellant management in space and submarine engine design. The accurate simulation of phase change phenomena in compressible flows requires a direct numerical solver thermodynamically consistent and able to describe the smallest driving scales and to handle capillary effects. The present solver has these characteristics. It solves the full system of conservation equations for real fluid compressible flows of single species written in primitive variables using a semi-implicit pressure based solver. It leads to the energy equation being a Screened Poisson equation for the pressure that can be solved as a linear system. For the sake of thermodynamic consistency, several cubic equations of state are proposed to describe liquid and vapour phases as well as evolving saturation conditions at the interface. The proposed solver can be considered as an extension of classical incompressible solvers for nucleate boiling based on sharp interface approaches towards configurations with temporally and spatially evolving saturation conditions at the interface. It enables a complete coupling between local liquid-vapour phase change at the interface and pressure variations due to local flow features or time evolving thermodynamic conditions. Its interest is demonstrated with several benchmarks of increasing complexity with an ultimate configuration involving bubble cavitation due to the pressure drop in a convergent pipe.

Quantitative comparison of dam break and bubble flows based on CF-VOF and IR-VOF schemes

In this study, an incompressible and immiscible two-phase flow solver was employed to assess the accuracy of phase-interface capturing methods in simulating two-phase flows. Three benchmark investigations were conducted involving two dam break flows with deformable free surfaces and the upward motion of a gas bubble through a liquid column. Four phase-interface capturing schemes, namely, MULES, HRIC and CICSAM from the Color Function Volume of Fluid (CF-VoF), and Interface Reconstruction Volume of Fluid (IR-VoF), were utilized. Comparative analysis of the phase interfaces indicated that CICSAM and IsoAdvector consistently provided sharp interfaces across all cases when compared to MULES and HRIC. The mass conservation performance of all schemes excelled in the dam-break case with relatively simple free-surface development and the rising bubble case. An examination of the local pressure distribution over time revealed that methods yielding diffusive interfaces produced inaccurate results. Thus, the importance of employing denser grids or schemes that yield sharper interfaces, such as CICSAM and IsoAdvector, to enhance simulation accuracy was underscored. Overall, the results of this analysis confirm that the IsoAdvector scheme, which provides sharp interfaces, is a reliable option for simulating incompressible immiscible two-phase flows.

Pressure Based Compressible Solver for Electric Arc-plasma Simulation

The electric arc discharge in a liquid medium is used in several applications such as the sterilization of the liquid by UV radiation, the fracturing of rocks by shock wave, the circuit breakers in oil bath or the forming of mechanical parts. Thus, describing the physics of the arc in a liquid and in particular its interaction with a liquid interface is an important issue to better characterize this type of configuration. However, such a challenging task requires to couple high-fidelity solver for compressible two-phase flows with liquid phase change and a plasma solver to describe the plasma and its interaction with the bubble. To study this type of medium, we use a compressible formulation of the fluid equations. For this purpose, a pressure based solver has been developed for the computation of the energy conservation equation. Moreover, our numerical model uses the immersed boundary method to simulate the solid electrodes. The numerical model is briefly described in this paper and the first results of the electric arc discharge in steam water are presented. To our knowledge this pressure based model has never been used to describe plasmas and electric arc discharge.

Three-Dimensional Flow Simulation by a Hybrid Two-Phase Solver for the Assessment of Liquid/Gas Transport in a Volute-Type Centrifugal Pump with Twisted Blades

A hybrid two-phase flow solver is proposed, based on an Euler–Euler two-fluid model with continuous blending of a Volume-of-Fluid method when phase interfaces of coherent gas pockets are to be resolved. In a preceding study on a two-dimensional bladed research pump with reduced rotational speed, the transition from bubbly flow to coherent steady gas pockets observed in optical experiments with liquid/gas flow could be well captured by the hybrid solver. In the present study, the experiments and solver validation are extended to an industrial-scale centrifugal pump with twisted three-dimensional blades and elevated design rotational speed. The solver is combined with a population balance model, and a scale-adaptive turbulence model is employed. Compared to the two-dimensional bladed pump, the transition from agglomerated bubbles flow to attached gas pockets is shifted to larger gas loading, which is well captured by the simulation. The pump head drop with increasing gas load is also reproduced, showing the hybrid solver’s validity for realistic pump operation conditions.

Numerical Investigation of Cavitation Bubble Jet Dynamics near a Spherical Particle

Synergistic interaction between cavitation bubbles and particles is critical for the operational performance of hydro turbines. The jet dynamics near the wall have been extensively investigated; however, the jet dynamics near the particles are not clear. In the present paper, the bubble jet dynamics near a spherical particle are numerically investigated based on a compressible two-phase flow solver considering the effects of heat transfer and mass transfer between the phases. Furthermore, the effect of the distance between the particle and the initial position of the bubble on the jet characteristics is analyzed in detail. Based on the simulations, three typical cases (i.e., jet during the rebound stage, jet pointing towards the particle, two jets facing each other) of jet behavior are categorized together with the range of dimensionless parameters. As the distance between the particle and the bubble increases, the three cases of jet impacts occur in the rebound stage, in the first period, and in the transition from the first period to the rebound stage, respectively.

Powering performance prediction of a semi-displacement ship retrofitted with Hull Vane

This study predicts the powering performance of a semi-displacement ship, both without and with a Hull Vane (HV). HV is an energy-saving appendage fixed at the transom bottom of the ship's hull. Although the HV is commercially known as a successful resistance-reducing device, there are no studies in the literature examining its effect on propulsion performance in detail. In this study, the effect of the HV on the propulsion performance is investigated and a practical method is proposed as an engineering application to reduce the computation time. Initially, the idealized disc model based on Blade Element Theory (BET) is preferred to create a thrust force instead of using an entire physical propeller. The dynamic motions of the ship are reflected in the computational analysis. Subsequently, the sliding mesh technique, which models the exact propeller geometry, is implemented to calculate the self-propulsion characteristics without and with HV. These computations are achieved by employing a two-phase flow solver available in OpenFOAM. This study provides a significant demonstration to clarify the effect of HV on powering performance. It not only decreases effective power by 11.41% but also increases the propulsive efficiency by 2.1%, which reduces the brake power by 14.61% in total at service speed.

A Level Set-Based Solver for Two-Phase Incompressible Flows: Extension to Magnetic Fluids

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier–Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number ≈ 1 ), while effectively preserving the mass conservation property. Subsequently, the numerical discretisation of Maxwell's equations under the magnetostatic assumption is described in detail, utilising the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilised for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh–Taylor instability growth in magnetic fluids.

A two-phase density-based solver for simulating wet steam flows with non-equilibrium condensation. II. Effects of 3D surface topography through nozzles

In Paper I, we developed a new two-phase flow solver and assessed its reliability and effectiveness through a series of numerical simulations. In Paper II, we utilized this solver to study the steam flow through nozzles characterized by three-dimensional surface topography. To generate random rough surfaces, we employed a multivariate Weierstrass–Mandelbrot function. Our numerical simulation results exhibited good agreement with the reported experimental data for pressure distribution. Moreover, we examined the changes in pressure, temperature, humidity, Mach number, average Nusselt number, and thrust as the wall surface morphology varied. We observed that the pressure field was prone to fluctuations, the boundary layer structure thickened and changed, the degree of condensation decreased with reduced humidity, three-dimensional Mach waves occurred, and the averaged Nusselt number decreased while thrust deviation increased. These findings contribute to a better understanding of the effects of fractal dimensions and condensation on random roughness in steam flow through nozzles and highlight the significance of incorporating surface topography into numerical simulations to improve accuracy and predictability in engineering applications.

Numerical Simulation of the Interaction between Solitary Waves and Underwater Barriers Using a VPM–THINC/QQ-Coupled Model

The interaction between solitary waves and underwater barriers is investigated using our in-house code, entitled VPM (volume-average/point-value multi-moment)–THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature)-coupled model. The stability and accuracy of the proposed model are validated by comparing the numerical results with those of the well established two-phase flow solver interFoam. All the results indicate that the presented coupled model has the advantage of high fidelity in simulating solitary wave propagation. Subsequently, solitary waves passing over a single underwater barrier are simulated by the present model. Numerical results are compared with experimental results in terms of the free surface elevation, velocity profile, vorticity field, and wave forces. Great agreements are obtained. In the end, the interactions between solitary waves and double underwater barriers are investigated numerically. The results reveal that the reflection coefficient increases first, and then decreases, with the increasing space between the two barriers. For cases with different wave heights, the transmission coefficient decreases monotonically, and the dissipation coefficient is opposed to the transmission coefficient.

Harmonic structure of the nonlinear force on a fixed ship-shaped floating production, storage and offloading vessel under dispersive phase-focused wave groups

This paper presents a numerical investigation on the harmonic structure of hydrodynamic forces on a fixed and simplified representative floating production, storage and offloading (FPSO) vessel hull under dispersive phase-focused wave groups. The high-fidelity numerical model utilizes the two-phase flow solver in the open-source toolbox OpenFOAM. A series of cases were computed using the numerical model, where the effects of wave steepness, bow diameter, and length of the FPSO are investigated. It is found that given an FPSO under different wave steepness, the non-dimensional inline force exhibits remarkable similarity in terms of the temporal development. The harmonic structure of the inline force is only weakly dependent on the steepness of the incident wave group and the bow diameter, but strongly dependent on the FPSO length. When k p L = 2.27, where L is the length of the FPSO and kp is the wave number at peak frequency, the incident wave group is diffracted significantly by the FPSO. The entire wave–structure interaction process is largely linear, where transfer between different harmonics is rarely seen. However, when kpL is further reduced to 0.57, globally the disturbance of the FPSO on the far field incident wave group is reduced, but locally a strongly nonlinear flow occurs at the rear of the FPSO, where severe run-up occurs at the downstream stagnation point. Higher-order harmonics of inline forces are excited, and the interaction process becomes much more nonlinear.

On the effects of hybrid surface wettability on the structure of cavitating flow using implicit large eddy simulation

BackgroundSupercavitation flow is characterized by the presence of a supercavity, which can be unstable and cause unwanted motion or even loss of control of an object. To address this issue, flow control techniques are often employed. These techniques aim to manipulate the flow of liquid around the object and improve stability and control. Some of these methods include using control surfaces, injecting fluids, or more advanced techniques such as active flow control or smart materials. MethodThe aim of this study is to use computational methods to investigate the behaviour of supercavitation flow over a Clark-Y hydrofoil with different contact angle patterns (hybrid wettability) inspired by the Namib desert beetle. The hybrid wettability consists of six distinct patterns with a 160-degree contact angle for superhydrophobic surfaces and a five-degree contact angle for superhydrophilic surfaces. To predict the dynamic and unsteady behaviours of the supercavitation flow with a cavity number of 0.4, the implicit large eddy simulation (ILES) technique and Kunz mass transfer model are used. The compressive volume of fluid technique is used in conjunction with dynamic adaptive mesh refinement to track the interface between the vapour and liquid phases. The simulations are conducted using the interPhaseChangeFoam two-phase flow solver within the OpenFOAM framework. This study analyses the time-averaged and instantaneous fluid dynamic properties of the supercavitation flow of the hydrofoil with a hybrid surface, including pressure, velocity, vorticity fields, wake flow, recirculation zone, and liquid volume fraction. In addition, it examines the instantaneous cavity leading edge and flow separation, the vortical flow structure, vorticity stretching and dilatation, spanwise flow details, the creation of a low-pressure zone behind the hybrid hydrofoil, streamwise velocity fluctuations, and the cavity dynamics over an entire cycle. FindingsThe results show that the contact angle has a significant effect on the structure of the supercavitation flow. Specifically, the use of a superhydrophobic surface on the pressure side and trailing edge of a hydrofoil, along with a superhydrophilic surface on the leading edge, can reduce the thickness of the wake zone, the length of the cloud cavity, and flow instability. Additionally, this approach can delay the onset of cavitation.

A Review of Preconditioning and Artificial Compressibility Dual-Time Navier–Stokes Solvers for Multiphase Flows

This review paper aims to summarize recent advancements in time-marching schemes for solving Navier–Stokes (NS) equations in multiphase flow simulations. The focus is on dual-time stepping, local preconditioning, and artificial compressibility methods. These methods have proven to be effective in achieving high time accuracy in simulations, as well as converting the incompressible NS equations into a hyperbolic form that can be solved using compact schemes, thereby accelerating the solution convergence and allowing for the simulation of compressible flows at all Mach numbers. The literature on these methods continues to grow, providing a deeper understanding of the underlying physical processes and supporting technological advancements. This paper also highlights the imposition of dual-time stepping on both incompressible and compressible NS equations. This paper provides an updated overview of advanced methods for the CFD community to continue developing methods and select the most suitable two-phase flow solver for their respective applications.

An AMR-Based Liquid Film Simulation with Surfactant Transport Using PLIC-HF Method

In this study, an AMR-PLIC-HF method is proposed and implemented by GPU parallel computing based on CUDA programming language and NVIDIA GPU. The present method improves the computation efficiency without compromising the accuracy and conservation of the volume. To satisfy the requirements of stencil points of the PLIC-HF method, an extended stencil computation method based on the tree-based AMR method is proposed and implemented. The Weakly Compressible Scheme (WCS) is used in the present work as a fluid solver. An evolving pressure projection method is adopted to suppress the oscillation induced by the reflection of acoustic waves. The Langmuir model is introduced into the solver to calculate surfactant transport and the Marangoni effect caused by the gradient of the interface concentration of the surfactant. The single vortex flow results verify the accuracy of the AMR-PLIC method. A single bubble rising problem with two different physical property settings is simulated. The results show good agreement with the results given by incompressible solvers. This verifies the accuracy of the two-phase flow solver including the AMR-PLIC-HF method and the WCS. The generation and rupture of liquid film by a single bubble freely rising to an interface is simulated by the present solver with a 1024×2048 AMR grid as the finest resolution. This simulation successfully calculates surfactant transport and the Marangoni effect.

Probabilistic analysis of irregular wave runup on a fixed and truncated surface-piercing vertical cylinder

This paper presents a numerical and experimental study on irregular wave runup on a fixed and truncated surface-piercing vertical cylinder. The numerical model was set up based on the incompressible two-phase flow solver in the open-source toolbox OpenFOAM. The model was successfully validated against the experimental data on both regular and irregular incident wave and wave runup. We analyse the characteristics of the runup spectrum against different kpHs and kpD, where kp is the wave number at peak frequency, Hs is the significant wave height and D is the diameter of the cylinder. A new method is proposed to predict the distribution of runup height. In this method, the average height of the highest one-third of all wave runup R1/3 is calculated based on the expansion of an empirical formula proposed in Cao et al., (2017). Then the non-dimensional runup height R/R1/3 is fitted into a two-parameter Weibull distribution, where the shape parameter and scale parameter are provided as a function of kpHs and kpD based on the interpolation of the experimental and numerical data. Based on the fitted Weibull distribution, the runup height at any cumulative probability can be determined. This newly proposed method is validated against the numerical and experimental data on the 2% excess wave runup height R2%, and the deviations are found to be within ±15% for most of the cases. Finally, a sensitivity analysis is conducted to demonstrate that the model uncertainty is within 15%.

Consistency and accuracy in the simulation of two-phase flows with phase change using sharp interface capturing methods

In this paper, the modeling of phase change in an incompressible two-phase flow solver is detailed without restricting the numerical methods to a specific interface capturing method. Starting from existing methodologies of the literature, the present work gives a step-by-step investigation of each numerical aspect of phase change to obtain an accurate and consistent solver.The main challenge when including phase-change is the handling of flux discontinuities at the interface when advancing temperature and species mass fraction. An accurate and second order discretization is proposed for any Eulerian representation of the interface either by adding a sharp source term or by imposing a boundary condition at the interface. As the accuracy and convergence rate of such solver are driven by the reconstruction of the evaporation rate m˙, particular attention is devoted to the reconstruction of gradient normal to the interface. Several methodologies are proposed to compute second-order gradients at the interface location adapted to any interface representation. Applying such techniques to a second-order accurate field leads to an expected first order accuracy of m˙ but with remarkable accuracy improvements using ghost cell methods with quadratic extrapolation. Then, several phase-change procedures are built by combining a selection of numerical methods to handle flux discontinuities and evaluate gradients. The procedures are investigated on planar phase-change simulations to bring out inconsistent combination choices. Finally, a multidimensional evaporation test case is presented to show the final accuracy and limitations of phase-change modeling in today two-phase flow solvers.

JAX-Fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are omnipresent in nature and engineering applications, and their accurate simulation is essential for providing insights into these processes. While PDEs are typically solved with numerical methods, the recent success of machine learning (ML) has shown that ML methods can provide novel avenues of finding solutions to PDEs. ML is becoming more and more present in computational fluid dynamics (CFD). However, up to this date, there does not exist a general-purpose ML-CFD package which provides 1) powerful state-of-the-art numerical methods, 2) seamless hybridization of ML with CFD, and 3) automatic differentiation (AD) capabilities. AD in particular is essential to ML-CFD research as it provides gradient information and enables optimization of preexisting and novel CFD models. In this work, we propose JAX-Fluids: a comprehensive fully-differentiable CFD Python solver for compressible two-phase flows. JAX-Fluids is intended for ML-supported CFD research. The framework allows the simulation of complex fluid dynamics with phenomena like three-dimensional turbulence, compressibility effects, and two-phase flows. Written entirely in JAX, it is straightforward to include existing ML models into the proposed framework. Furthermore, JAX-Fluids enables end-to-end optimization. I.e., ML models can be optimized with gradients that are backpropagated through the entire CFD algorithm, and therefore contain not only information of the underlying PDE but also of the applied numerical methods. We believe that a Python package like JAX-Fluids is crucial to facilitate research at the intersection of ML and CFD and may pave the way for an era of differentiable fluid dynamics. Program summaryProgram title: JAX-FluidsCPC Library link to program files:https://doi.org/10.17632/pzvkwn5s6p.1Developer's repository link:https://github.com/tumaer/JAXFLUIDSCode Ocean capsule:https://codeocean.com/capsule/6819679Licensing provisions: GNU GPLv3Programming language: PythonSupplementary material: Source code; Examples; Videos: Moving solid bodies, Taylor-Green vortex, Rising bubble, Shock-bubble interaction.Nature of problem: The compressible Navier-Stokes equations describe continuum-scale fluid flows. These flows often involve highly complex flow phenomena such as shocks, material interfaces, and turbulence. The intrinsic nonlinear dynamics render the numerical simulation of the these equations challenging. Machine learning provides novel avenues for describing partial differential equations. Machine learning models rely on gradient information provided by automatic differentiation and are often implemented in Python. In contrast, existing high-performance computational fluid dynamics codes are typically written in Fortran or C++ and do not offer inherent automatic differentiation capabilities. These discrepancies hinder the advance of machine-learning-supported computational fluid dynamics. Up to this day, a general-purpose fully-differentiable computational fluid dynamics solver for compressible two-phase flows is missing.Solution method: We introduce JAX-Fluids: a general-purpose three-dimensional fully-differentiable computational fluid dynamics solver for compressible two-phase flows. JAX-Fluids is a simulation framework intended for machine-learning-supported computational fluid dynamics research. Our framework is written entirely in JAX, a high-performance numerical computing library with automatic differentiation capabilities. We have used an object-oriented programming style and a modular design philosophy. This allows the straightforward exchange of numerical methods. We provide a wide variety of state-of-the-art high-order computational methods for compressible flows. The modularity of our framework additionally facilitates the integration of custom subroutines. We use the sharp-interface level-set method to model two-phase flows. The software package can easily be installed as a Python package. We have build the source code around the JAX NumPy API. This makes JAX-Fluids accessible and performant. JAX-Fluids runs on CPUs, GPUs, and TPUs. We use HDF5 in combination with XDMF for writing output quantities. The Python packages Haiku and Optax are used for implementation and training of machine learning methods.Additional comments including restrictions and unusual features: JAX-Fluids relies on open-source third-party Python libraries. These are automatically installed. In the current version, JAX-Fluids only runs on a single accelerator (CPU/GPU/TPU). Future versions will include support for parallel execution. JAX-Fluids has been tested on Linux and macOS operating systems.

Fast Multigrid Algorithm for Non-Linear Simulation of Intact and Damaged Ship Motions in Waves

This paper proposes a fast multigrid algorithm to simulate the non-linear motion of ships in both intact and damaged conditions. The simulations of ship motions in waves are known to require much time to calculate due to the strong non-linear interactions between ship and waves. To improve the calculation efficiency while retaining the accuracy, a prediction-correction strategy was designed to accelerate the simulation through three sets of locally refined meshes. The flow field was first estimated in a coarse mesh and then mapped to a locally refine mesh for further higher-fidelity corrections. A partitioned radial basis function (PRBF) method is proposed to interpolate and reconstruct the flow field for the refined mesh. A new two-phase flow solver was developed with a fast multigrid algorithm based on the Reynolds-averaged Navier–Stokes equations (RANSE). The new solver was applied to study the non-linear behavior of a damaged ship in beam waves and the effect of damaged compartments on ship rolling motion. Validation against the solution with the original method of single set meshes and experimental data indicates that the proposed algorithm yields satisfactory results while saving 30–40% of the computational time.