Finite Volume Research Articles

Mixed Convection of an Ag/Water Nanofluid in a Ventilated Square Cavity Containing Cold Blocks of Different Shapes

This research presents the results of a numerical study on mixed convection in a ventilated cavity with a central cold block of varying shapes. The direction of the forced flow of Ag/water nanofluid is perpendicular to the transverse axis (y) of the central cold block. Mixed convection is induced by cooling at the entrance of the ventilated cavity and uniformly heating its bottom wall. The governing equations for the flow of an incompressible Newtonian nanofluid are assumed to be two-dimensional, steady, and laminar. The finite volume method is employed for numerical simulations. A series of calculations are conducted to investigate the effects of key influencing factors: Reynolds number (Re = 100), Richardson number (Ri = 1), and nanoparticle volume fractions (0 ≤ ∅ ≤ 8%) on the enhancement of heat transfer. The impact of four different geometric shapes of the cold obstacle (circular, square, triangular, and elliptical) on fluid flow and heat transfer rate is also explored. The results indicate that an increase in nanoparticle volume fraction enhances the heat exchange rate in the cavity only when the geometric shape of the cold obstacle is circular. This is followed by square and triangular shapes, which approximately yield concordant results, and then the elliptical shape.

High-order genuinely multidimensional finite volume methods via kernel-based WENO

In this paper a family of fully multidimensional kernel-based reconstruction schemes for use in finite volume methods (FVMs) will be presented. These methods are intended for use in shock dominated problems, and stability is achieved through a suitable adaptation of the Adaptive Order Weighted Essentially Non-Oscillatory (WENO-AO) method to the proposed kernel-based reconstruction schemes. There are a number of key difficulties in the design of high-order finite volume schemes which will be discussed and addressed. High (4th and 6th) order convergence will be demonstrated on smooth exact solutions of the ideal MHD equations. The very same scheme will then be applied to extremely stringent astrophysical benchmark problems.

Numerical simulation of fluid-vegetation coupled dynamic using a promoted semi-resolved coupling model

Flexible vegetation is an important component of riverine and coastal ecosystems. The numerical simulation is difficult due to the complex motions of flexible vegetation and fluid. In this work, a semi-resolved numerical model coupling the computational fluid dynamics (CFD) and flexible rod dynamics (FRD) using a promoted two-way domain expansion method was proposed with the accuracy of the resolved model and the efficiency of the unresolved model. The governing equations of the flexible rod dynamics are solved by the finite element method (FEM). The effect of vegetation is added as source terms to the Reynolds-averaged Navier-Stokes equations, which are discretized and solved by the finite volume method (FVM). The anisotropic Gaussian kernel function is adopted to calculate the interactive forces between the fluid and the flexible rod with an anisotropic cross-section. The model was first validated by simulating the flow passing through a single flexible rod with a rectangular cross-section. Meanwhile, the main factors were calibrated. The engineering application of the model was further validated by simulating the flow passing through a finite patch of flexible vegetation. These results indicate that the proposed model could well simulate the open channel flows with the flexible vegetation.

Predicting unsteady incompressible fluid dynamics with finite volume informed neural network

The rapid development of deep learning has significant implications for the advancement of computational fluid dynamics. Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced accuracy in predicting boundary layer flows and poor adaptability to geometric shapes. Although graph neural network models for unstructured grid-based unsteady flow prediction have better geometric adaptability, these models suffer from error accumulation in long-term predictions of unsteady flows. More importantly, fully data-driven models often require extensive training time, greatly limiting the rapid update and iteration speed of deep learning models when facing more complex unsteady flows. Therefore, this paper aims to balance the demands for training overhead and prediction accuracy by integrating physical constraints based on the finite volume method into the loss function of the graph neural network. Additionally, it incorporates a twice-message aggregation mechanism inspired by the extended stencil method to enhance the unsteady flow prediction accuracy and geometric shape generalization ability of the graph neural network model on unstructured grids. We focus particularly on the model's predictive accuracy within the boundary layer. Compared to fully data-driven methods, our model achieves better predictive accuracy and geometric shape generalization ability in a shorter training time.

The effect of the laser beam intensity profile in laser-based directed energy deposition: A high-fidelity thermal-fluid modeling approach

Modeling the thermal and fluid flow fields in laser-based directed energy deposition (DED-LB) is crucial for understanding process behavior and ensuring part quality. However, existing models often fail to accurately predict these fields due to simplifying assumptions, particularly regarding powder particle-induced attenuation in laser power and energy density distribution, and the variable material properties and process parameters. The present work introduces a high-fidelity multi-phase thermal-fluid model driven by a combination of the discrete element method (DEM) and the finite volume method (FVM). Incorporating an enhanced attenuation model for laser energy enables a more precise approximation of powder particle-induced attenuation effects in the laser power and energy density distribution. The study focuses on the influence of laser beam intensity profiles during DED-LB of austenitic stainless steel (AISI 316 L), with model validation conducted through experimental measurements of deposited track dimensions for different beam shapes. The results of numerical simulations demonstrate the critical impact of powder-induced attenuation on the laser power and intensity profiles. Neglecting laser energy attenuation, a common assumption in numerical simulations of DED-LB, leads to overestimations of the absorbed energy of the laser beam, affecting thermal and fluid flow fields, and melt pool dimensions. The present study unravels the complex relationship between the attenuation coefficient (due to the powder stream) and powder stream characteristics, describing the variations of the attenuation coefficient with changes in the powder mass flow rate and powder stream incidence angle. The findings show the critical effects of laser beam shaping on melt pool behavior in DED-LB, with square beams inducing larger melt pool volumes and circular beams creating smaller but deeper melt pools. The proposed enhanced thermal-fluid modeling framework offers a robust approach for optimizing laser-based additive manufacturing across diverse materials and laser systems.

A numerical simulation method for solving electromagnetic-mechanical coupling field

A new numerical simulation method based on the finite volume method has been proposed to address the challenges associated with the pseudo-oscillation phenomenon that occurs with an increased Péclet number, as well as determining an appropriate time step for electromagnetic-mechanical coupled physical field calculations. This method utilizes the concept of upwind from Computational Fluid Dynamics (CFD) to solve Maxwell's equations, a finite-volume method for discretizing the electromagnetic diffusion equations. Through computing typical electromagnetic field problems such as TEAM problem 9–1 and comparing the results to the literature, it has been confirmed that this method has sufficient computational accuracy to solve electromagnetic field numerical simulation problems containing moving conductors. Additionally, a three-dimensional simulation model of the electromagnetic coil gun has been established to verify the viability of the proposed method for solving magnetic field problems under the electromagnetic launch (EML) system. The study also examined the change in magnetic field strength and current density of the EML device during the launching process. The results lay the foundation for the technical application of this method.

Improved hybrid approach of monotonic upstream-centered scheme for conservation laws and discontinuity sharpening technique for steady and unsteady flows

In finite-volume methods, monotonic upstream-centered schemes for conservation laws (MUSCL) offer second-order spatial accuracy but tend to produce highly dissipative solutions for density discontinuity and weak shock waves. To address this limitation within a second-order framework, a novel strategy for hybridizing MUSCL with the tangent of the hyperbola interface capturing technique for both steady and unsteady compressible flows is presented. This hybridization optimizes the process based on the degree of nonlinearity and discontinuity around the target cells, providing a novel method to sharply resolve weak shock waves and robustly compute strong shock waves within the hybrid scheme. The proposed scheme sharply captures exceedingly weak shock waves that conventional MUSCL fails to resolve accurately due to excessive numerical dissipation. Furthermore, for resolving small vortices induced by instability at slip lines, computational results demonstrate high-resolution surpassing fifth-order spatial accuracy schemes within this second-order spatial accuracy framework with less computational cost. Moreover, the scheme exhibits commendable convergence and robustness when applied to steady-state problems featuring strong shock waves. This scheme offers a more precise and high-resolution alternative to conventional MUSCL for compressible flow computations, as it requires no additional stencil for reconstruction, unlike conventional fifth-order schemes.

Performance study of variational quantum linear solver with an improved ansatz for reservoir flow equations

This paper studies the performance of the variational quantum linear solver (VQLS) with an improved ansatz for discretized reservoir flow equations for the first time. First, we introduce the two typical flow equations in reservoir simulation, namely, the diffusion equation for pressure and the convection-dominated Buckley–Leverett equation for water saturation, and their commonly used finite volume or finite difference-based discretized linear equations. Then, we propose an improved ansatz in VQLS to enhance the convergence and accuracy of VQLS and a strategy of adjusting grid order to reduce the complexity of the quantum circuit for preparing the quantum state corresponding to the coefficient vector of the discretized reservoir flow equations. Finally, we apply the modified VQLS to solve the discretized reservoir flow equations by employing the Xanadu's PennyLane open-source library. Four numerical examples are implemented, and the results show that VQLS can calculate reservoir flow equations with high accuracy, and the improved ansatz significantly outperforms the original one. Moreover, we study the effects of reservoir heterogeneity, the number of ansatz layers, the equation type, and the number of shots on the computational performance. Limited by the current computing capacity, the number of grids subject to the involved number of quantum bits in the implemented examples is small; we will further explore this quantum algorithm to practical examples that require a large number of quantum bits in the future.

On wave-current interaction with a horizontal cylinder near free surface by a fourth-order-accurate finite volume compact solver

We present a numerical solver for dealing with the problem of wave-current interaction with a horizontal cylinder near free surface. The solver solves the filtered Navier-Stokes equations which are discretized using a fourth-order-accurate compact finite volume scheme on a collocated grid. The turbulence effect is modelled by a subgrid-scale model using a large eddy simulation, and the free surface and the cylinder are modelled by a volume of fluid method and a ghost cell immersed boundary method. The pressure-velocity coupling is ensured via a momentum interpolation method. We obtain the hydrodynamic force and its spectra characteristics, dynamic pressure distribution, streamline topology and vorticity patterns with different immersed depths under uniform currents, regular waves and wave-current flows. Validation is performed by comparing the calculated hydrodynamic force with the measured data within one wave period. The results show that the position of vortex shedding and dissipation is different for the cases under different immersed depth in regular waves and wave-current flows. The dynamic pressure around the cylinder as the force reaches its peak value changes with immersed depth. The value and phase of the force are sensitive to immersed depth.

A Verification Suite of Test Cases for the Barotropic Solver of Ocean Models

AbstractThe development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs designed to verify the barotropic solver of atmosphere and ocean models. These include the non‐dispersive coastal Kelvin wave; the dispersive inertia‐gravity wave; the dispersive planetary and topographic Rossby waves; the barotropic tide; and a non‐linear manufactured solution. These TCs check the implementation of the linear pressure gradient term; the linear constant or variable‐coefficient Coriolis and bathymetry terms; and the non‐linear advection terms. Simulation results are presented for a variety of time‐stepping methods as well as two spatial discretizations: a mimetic finite volume method based on the TRiSK scheme, and a high‐order discontinuous Galerkin spectral element method. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions.

Influences of coriolis force and friction on fluid dynamics in specific paraboloid basins

Natural water features, such as rivers, lakes, bays, and straits, exhibit diverse shapes and dynamics. Among these, paraboloid basins, resembling the contours of lakes or closed bays, offer a relatively simple yet intriguing case. This study delves into the dynamics of water waves within two distinct paraboloid basin variations: the parabolic canal and the circular paraboloid. In this investigation, we analyze shoreline movement, considering influential factors such as bottom friction and the Coriolis effect through a mathematical model. The foundation of our analysis lies in the two-dimensional shallow water equations, with the Thacker assumption serving as the basis for deriving an analytical solution. To enhance our understanding, we employ a numerical solution, employing the finite volume method on a staggered grid, to simulate wave behavior within these basin variations. For validation, we compare these numerical findings with our analytical solution. Furthermore, this study conducts a sensitivity analysis of the Coriolis parameter and bottom friction parameter under various conditions. Through this exploration, we gain valuable insights into the interplay of these critical factors in shaping the oscillation of water within paraboloid basins, enriching our understanding of coastal and basin dynamics.

Estimation of Thermal Properties of Solid–Liquid Phase Change Material Using Fuzzy Inference Methods

The accurate measurement of thermal properties in phase change materials holds significant importance for engineering applications. This research introduces fuzzy inference methods to estimate the thermal properties of phase change materials. The solution to the coupled heat transfer involving radiation and conduction in material is achieved through a hybrid approach, which combines the finite volume method with the discrete ordinate method. The estimation process is structured as an inverse problem, where the temperature on the material surface acts as the measurement signal for conducting the inverse analysis. Both the fuzzy inference method and the decentralized fuzzy inference method are utilized to address the inverse heat transfer problem. This enables the determination of latent heat and thermal conductivities for both solid and liquid regions within the phase change material. Retrieval results demonstrate that the thermal properties of phase change materials can be accurately estimated using fuzzy inference methods. While both two fuzzy inference methods perform similarly in estimating a single parameter, the fuzzy inference method has limitations in multiparameter estimation tasks. Conversely, the decentralized fuzzy inference method yields accurate results in simultaneous estimation problems. Furthermore, this method proves robust in estimating the thermal properties of phase change materials, even in the presence of noisy data.

Predicting reattaching turbulent gas-solid flow with a strong pressure gradient

In this study, the focus is on examining how the flow characteristics are influenced by particle density in the context of downward turbulent gas-solid flow through a sudden expansion pipe. The Eulerian-Lagrangian approach is performed to simulate the gas and the solid phases. A self-written FORTRAN code is developed based on the finite volume technique with a hybrid scheme in a staggered grid to simulate the problem. Experimental measurements and numerical simulations are employed to study the flow dynamics. After comparing the outcomes with previously published experimental findings, the current code demonstrates favorable results that provide encouragement for the authors to expand their theoretical work and explore various parameters. The sudden expansion performance is studied at different particle materials (sodium, sand, aluminum, copper, and gold) and Reynolds numbers. In light of the computational results, the particle material has a significant influence on the flow behavior. As the particle density increases from sodium to gold, the solid phase becomes more concentrated and exhibits different flow patterns. The particle density also affects the pressure distribution, velocity profiles, and turbulent kinetic energy in the flow. The particle size significantly influences both the flow behavior and the loss coefficient.

2D unified atmosphere and wind simulations of O-type stars

Context. Massive and luminous O-type star (O star) atmospheres with winds have been studied primarily using one-dimensional (1D), spherically symmetric, and stationary models. However, observations and theory have suggested that O star atmospheres are highly structured, turbulent, and time-dependent. As such, when making comparisons to observations, present-day 1D modeling tools require the introduction of ad hoc quantities such as photospheric macro- and microturbulence, wind clumping, and other relevant properties. Aims. We present a series of multi-dimensional, time-dependent, radiation-hydrodynamical (RHD) simulations for O stars that encapsulate the deeper sub-surface envelope (down to T ~ 450 kK), as well as the supersonic line-driven wind outflow in one unified approach. Our overarching aim is to develop a framework that is free from the ad-hoc prescriptions that plague present-day 1D models. Here, we start with an analysis of a small set of such multi-dimensional simulations and then compare them to atmospheric structures predicted by their 1D counterparts. Methods. We performed time-dependent, two-dimensional (2D) simulations of O star atmospheres with winds using a flux-limiting RHD finite volume modelling technique. Opacities are computed using a hybrid approach combining tabulated Rosseland means with calculations (based on the Sobolev approximation) of the enhanced line opacities expected for supersonic flows. The initial conditions and comparison models were derived using similar procedures as those applied in standard 1D stationary model atmosphere with wind codes. Results. Structure starts appearing in our simulations just below the iron-opacity peak at ~200 kK. Local pockets of gas with radiative accelerations that exceed gravity then shoot up from these deep layers into the upper atmosphere, where they interact with the line-driven wind outflow initiated around or beyond the variable photosphere. This complex interplay creates large turbulent velocities in the photospheric layers of our simulations, on the order of ~30–100km s−1, with higher values for models with higher luminosity-to-mass ratios. This offers a generally good agreement with observations of large photospheric ‘macroturbulence’ in O stars. When compared to 1D models, the average structures in the 2D simulations display less envelope expansion and no sharp density-inversions, along with density and temperature profiles that are significantly less steep around the photosphere, and a strong anti-correlation between velocity and density in the supersonic wind. Although the wind initiation region is complex and highly variable in our simulations, our average mass-loss rates agree well with stationary wind models computed by means of full co-moving frame radiative transfer solutions. Conclusions. The different atmospheric structures found in 2D and 1D simulations are likely to affect the spectroscopic determination of fundamental stellar and wind parameters for O stars as well as the empirical derivation of their chemical abundance patterns. To qualitatively match the different density and temperature profiles seen in our multi-dimensional and 1D models, we need to add a modest amount of convective energy transport in the deep sub-surface layers and a large turbulent pressure around the photosphere to the 1D models.

Numerical aspects of modeling flow through the cerebral artery system with multiple small perforators

This study investigates the flow and hemodynamics of small perforator blood vessels that branch from the basilar artery (BA) in the brain. Using advanced imaging techniques and computational fluid dynamics (CFD) simulations, detailed 3D geometries of the perforators were acquired through barium contrast injection, micro-CT scans, and data processing. The hybrid geometry, combining micro-CT scans and mesh extraction algorithms, provided accurate vessel models. The influence of different types of finite volume on the analysis was examined, with polyhedral elements showing the most efficient ratio of the analysis time to convergence level. Additionally, the effect of boundary conditions on hemodynamic parameters was studied. Simulations using 0.0 mmHg pressure conditions at the outlets directed flow mainly through the BA, neglecting the perforator branches. In contrast, non-zero outlet pressure conditions significantly increased the flow in the perforators, leading to non-physiological flow velocities and overestimation of hemodynamic parameters. The assumption of pressure conditions of 0 mmHg at outlets was found to be valid for simple single vessel geometries, but not for more complex vascular systems. This research contributes valuable information on the complex flow patterns and hemodynamics of small perforator blood vessels in the brain and emphasizes the importance of accurately modeling geometry and boundary conditions in such studies.

Development and benchmarking of space-time kinetics solver in REDAC

A space–time kinetics solver based on finite volume approach has been developed for REactor Dynamics Analysis Code (REDAC). It solves 3D multi-group neutron diffusion equation, coupled with the heat transport equations. Code offers flexibility in terms of reactor geometry, boundary conditions and discretization. Efficient numerical methods have been employed for solving the governing equations. The performance of the code has been demonstrated by solving diverse benchmark problems. It is shown that REDAC is able to predict important static and dynamic core parameters with good accuracy. The framework of REDAC easily lends itself for sensitivity studies with respect to spatial discretization and temporal integration schemes. From these studies, it is observed that spatial resolution could have significant influence on accuracy and the semi-implicit method performs better than the implicit method. Improved quasi-static method requires less computational time compared to the direct method, however, its accuracy depends on the time step size.

Improving Global Barotropic Tides With Sub‐Grid Scale Topography

AbstractIn recent years, efforts have been made to include tides in both operational ocean models as well as climate and earth system models. The accuracy of the barotropic tides is often limited by the model topography, which is in turn limited by model horizontal resolution. In this work, we explore the reduction of barotropic tidal errors in an ocean general circulation model (Modular Ocean Model version 6; MOM6) using sub‐grid scale topography representation. We follow the methodology from Adcroft (2013, https://doi.org/10.1016/j.ocemod.2013.03.002), which utilizes statistics from finer resolution topographic data sets to represent sub‐grid scale features with a light computational cost in a structured finite volume formulation. The geometric effect from sub‐grid scale topography can be introduced to the model with only a few parameters at each grid cell. The porous barriers, which are implemented at the walls of the grid cells, are used to modify transport between grid cells. Our results show that the globally averaged tidal error in lower‐resolution simulations is significantly reduced with the use of porous barriers. We argue this method is a potentially useful tool to improve simulations of tides (and other flows) in low‐resolution simulations.

Research on Wave-Added Resistance and Longitudinal Stability Characteristics of Amphibious Aircraft in Rule Wave

Assessing the safety of amphibious aircraft hinges significantly on two key factors: wave-added resistance and motion stability during takeoff and landing on water surfaces. To tackle this, we employed the Reynolds-averaged Navier–Stokes (RANS) equations solved via the finite volume method. We utilized the volume fraction method to accurately capture the free surface and employed the overset grid technique to manage the relative motion between the aircraft and the liquid surface. Our approach involves establishing a numerical simulation scheme to investigate the water-planing motion of amphibious aircraft across varying wave heights, wavelengths, speeds, and center-of-gravity positions. The computational findings demonstrate a close match between calculated forces and aircraft motion compared to experimental values. Notably, we observed pronounced nonlinearity in wave-added resistance. Under high sea conditions, operating in a short-wavelength environment or with a rearward center-of-gravity position proves advantageous for reducing wave-added resistance. Conversely, poor longitudinal stability is evident during planing in long waves.

Cooling effectiveness enhancement of parallel air-cooled battery system through integration with multi-phase change materials

This work presents a numerical investigation of the integration of conventional parallel air-cooling battery system with multi-phase change materials (PCMs) to improve the cooling effectiveness at low power consumption (Pc) rate. The study considers various cells partitioning of the PCMs on nine different parallel air-cooled battery packs. The impact of PCMs pattern schemes, inclination angle of the manifold, and air inlet velocity are analysed by employing finite volume technique coupled with an enthalpy-porosity method. Compared with a typical parallel air-cooling system, despite 90% reduction in the air inlet velocity, the integrated system successfully lowers the maximum temperature (Tmax) by 12.0 K and improves uniformity of temperature distribution based on standard deviation (SDV) of temperature field by 43.9%. Subsequently, inclining the air inlet manifold to an angle close to vertical leads to a poor cooling performance. Also, a proper pattern of PCMs cells partitioning having a trapezoidal cell shape at the top and bottom, and a parallelogram cell shape at the midsection exhibits a better heat dissipation performance. Moreover, compared to the module with highest inlet velocity of 1.5 m/s, reducing the inlet velocity by 66.7% still controls Tmax at 313.13 K which is well below the critical limit, and decreases the Pc by 65.8%.

An explicit material point and finite volume sequentially coupled method for simulating large deformation problems in saturated soil

An explicit material point and finite volume sequentially coupled method (MPM-FVM) is developed using u-p form coupling formulations for the simulation of large deformations in saturated soil. In MPM-FVM, the momentum conservation equation is solved by MPM under the updated Lagrange framework, and the mass conservation equations are solved by FVM under the Euler framework. The numerical implementation of an explicit sequentially coupled algorithm is developed considering the tradeoffs between computational cost and numerical stability. The critical time step of u-p form governing equations is derived using the Von Neumann method, which is found to be much greater than the u-U form explicit MPM at low permeability, allowing for high numerical stability. Three numerical cases are presented to demonstrate the stability, efficiency, and effectiveness of the developed MPM-FVM method. The simulation of a saturated one-dimensional soil column subjected to quasi-static and dynamic loads validates the method, and highlights its greater efficiency and accuracy compared to standard solid–fluid coupled MPM methods. The large deformation simulation capability of the method is exhibited via simulation of a saturated slumping block. In real-world application, simulation results obtained using method achieves excellent agreement with the experiment measurements and observations of the Selborne landslide experiment.