Finite Volume Research Articles

Numerical Analysis and Validation of Horizontal and Vertical Displacements of a Floating Body for Different Wave Periods

This study concentrates on numerically evaluating the behavior of a floating body with a box format. Although research on floating objects has been conducted, the numerical modeling of Wave Energy Converter (WEC) devices, considering the effects of fluctuations, remains underexplored. Therefore, this research intends to facilitate the analysis of floating devices. First, the experimental data served as a benchmark for evaluating the motion paths of the floating box’s centroid. Second, the effects of various wave periods and heights on the floating body’s movement were analyzed. The Volume of Fluid (VOF) multiphase model was applied to simulate the interactions between phases. The computational model involved solving governing equations of mass conservation, volumetric fraction transport, and momentum, employing the Finite Volume Method (FVM). The validation demonstrated that the Normalized Root Mean Square Error (NRMSE) for the x/h ratio was 3.3% for a wave height of 0.04 m and 4.4% for a wave height of 0.1 m. Moreover, the NRMSE for the z-coordinate to the depth of water (z/h) was higher, at 5% for a wave height of 0.04 m and 5.8% for a wave height of 0.1 m. The overall NRMSE remained within acceptable ranges, indicating the reliability of the numerical solutions. Additionally, the analysis of horizontal and vertical velocities at different wave periods and heights showed that for H = 0.04 m, the wave periods had a minimal impact on the amplitude, but the oscillation frequency varied. At H = 0.1 m, both velocities exhibited significantly larger amplitudes, especially for T = 1.2 s and T = 2.0 s, indicating stronger motion with higher wave heights.

Thermodynamics and generalized hydrodynamics of simple integrable QFT in finite volume

Abstract We derive thermodynamic (TBA) and general hydrodynamic (GHD) equations corrected by virtual processes for integrable QFT on large but finite size space circle. Obtained TBA’s are solved numerically for the sinh-Gordon model. Complicated Euler scale GHD equations are expanded explicitly for small occupation ratio of virtual quasiparticles. The spectrum of velocities for the linear approximation to GHD is numerically calculated.

An analysis of the bilinear finite volume method for the singularly-perturbed convection-diffusion problems on Shishkin mesh

In this paper, we study the bilinear finite volume element method for solving the singularly perturbed convection-diffusion problem on the Shishkin mesh. We first prove that the finite volume element scheme is ϵ-uniformly stable. Then, based on new expression of the finite volume bilinear form and some detailed integral calculations, an ϵ-uniform error estimation is derived in the ϵ-weighted gradient norm, including the L2-norm. This error estimate is better than the known result. Moreover, we also give the L∞-error estimate near the boundary layer regions. At last, numerical experiments show the effectiveness of our method.

Assessment of the hydro-thermal performance for a novel hexagonal mini-channel heat sink for cooling a cylindrical heat source

Liquid cooling using a mini-channel heat sink (MHS) has been highly efficient in cooling rectangular and cylindrical lithium batteries. This work proposed a new hexagonal MHS (HMHS) to cool a cylindrical heat source instead of the traditional cylindrical with smooth MHS (CSMHS). In addition to the smooth channels, four obstructed channels were proposed to further enhance the thermal performance of this HMHS. The obstructions used include: semicircular ribs–cavities, semicircular ribs–secondary flow, semicircular pin fins and semicircular pin fins–cavities. This study was numerically conducted using the finite volume method under water Reynolds number ranging from 100 to 800. CSMHS and HMHS with semicircular pin fins were manufactured and tested to verify the validity of the numerical results. Results showed that the HMHS exhibited superior hydro-thermal performance compared with the CSMHS. In addition, the HMHS with obstructed channels contributes to a significant improvement in thermal performance. The percentages of Nusselt number improvement with all channels were approximately: 12.3%, 60.5%, 71.5%, 104% and 112% for smooth, semicircular ribs–cavities, semicircular rib–secondary flow, semicircular pin fins and semicircular pin fins–cavities, respectively. Amongst all the channels, the channels with semicircular pin fins achieved the best performance with a hydro-thermal performance factor of 1.67.

Impact of density ratio on droplet dynamics in pulsating flow

Secondary atomization is extensively studied by investigating a droplet subjected to a steady air/gas stream. However, droplets are often subjected to unsteady or pulsating flows, such as in aero-engines or rockets, because of thermo-acoustic instabilities in the combustion chambers. The investigation focuses on the droplet dynamics and breakup in a pulsating flow for a range of density ratios (ρr), 1000 to 10, under sinusoidal airflow of different amplitudes and frequencies as compared to the dynamics in a steady flow. The volume of fluid multiphase model tracks the liquid–gas interface, and the governing equations are solved using the finite volume method. The two-dimensional axisymmetric pulsating simulations demonstrate accuracy comparable to the corresponding three-dimensional simulations at a much lower computational cost and are used for parametric studies. The droplets under the pulsating flow show a wavy surface, and larger vortex structures are observed during the deceleration period. At a high-density ratio (1000), pulsating flow enhances droplet deformation for a faster breakup, with the flow amplitude having more impact than its frequency. For a medium-density ratio (100), where breakup occurs under steady flow, droplet breakup is inhibited in the pulsating flow at low amplitude and high frequency. In the case of a low-density ratio (10), there is no breakup under steady flow, but pulsating flow promotes breakup, except at low amplitude and high frequency. The droplet breakup is always achieved for the highest amplitude, while lower frequencies push the liquid mass from the center of the droplet to the rim.

Study Explores Fracture-Driven Interaction Mitigation Strategies for Field Development

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 4055561, “Numerical Investigation of Fracture-Driven-Interaction Mitigation Strategies and Field Development Optimization,” by Ruiting Wu, SPE, Xiaolong Liu, and Lili Xu, Chevron, et al. The paper has not been peer reviewed. _ Numerical modeling of fracture-driven interactions (FDI) using a coupled hydraulic-fracturing-propagation, reservoir-flow, and geomechanics tool has been conducted. The numerical study showed that, for the basins studied, FDI and some mitigation strategies have minimal effect on long-term parent-well productions. Parent depletion (volume and areal extent), well spacing, and child-fracture asymmetry, however, greatly affect child-well production as the result of FDI. Introduction Interwell FDI, also known as frac hits, has garnered recent attention given that more than 60% of new wells drilled in US unconventional reservoirs are infill drilling. Whereas uncontrollable parameters, such as natural fractures and matrix permeability, do contribute to the effect of FDI on well production, the authors’ primary focus lies on controllable factors. Field observations have shown that tighter well spacing and smaller completion sizes tend to result in fewer negative effects on both parent- and child-well production. Additionally, fracture-fluid injection rates, the number of clusters, and cluster spacing all influence FDI effects. Simulation Tool and Workflow A coupled hydraulic-fracture, reservoir, and wellbore simulator was used to simulate the fracturing and production stage of the parent and child wells and related fracture-driven well interaction. The simulator simultaneously solves the equations of fluid flow, proppant transport, water/solute transport, fracture mechanics, and poroelasticity in the well, fracture, and matrix domains. Fracture propagation is calculated using the multilayer-tip-elements algorithm. Fracture elements are represented by uniformly sized rectangles. Fracture-to-fracture stress shadow is calculated with the 3D displacement discontinuity method, and the poroelastic stress responses during fracture propagation and depletion are calculated with a finite-volume method. The tool is designed to simulate the entire life cycle of the FDI interaction. The modeling workflow also includes calibration with field observations of fracture geometry, the pressure response at the parent well during fracturing of the child well, the water cut change at the parent well as the result of FDI, and production performance. Field Case Study: Permian Basin The primary objective of this study is to identify the key parameters that contribute to FDI and mitigate the negative effects of FDI. Two field case studies were conducted in two basins, the Permian Basin and the DJ Basin. In both field studies, a history match of parent and child well performance was first conducted. Then, a sensitivity study was performed on various key parameters to understand their effects on the production performance at both parent and child wells. Both field case studies are focused on the lateral FDI. The first case study is included in this synopsis.

A novel relaxed modified pipe hydrodynamic model for mixed flow simulation

In this study, we propose a novel modified pipe hydrodynamic model with a partial relaxation approach and develop a corresponding numerical algorithm within the framework of the finite volume method for its computation to enable robust, accurate, and comprehensive pipe modeling. The proposed numerical model provides some key improvements compared to existing numerical schemes for simulating mixed pipe flows: (1) it is capable of preserving both moving- and stationary-water steady states, and (2) it effectively reduces post-bore oscillations while maintaining second-order accuracy in the non-pressurized regime for unsteady pipe flows. Such improvements have been verified against theoretical and experimental data through tests involving both smooth and sharp-gradient steady and unsteady flows across various regimes in straight and locally bent circular pipes, which are fundamental elements of stormwater drainage, sewage networks, and industrial process pipelines. The proposed pipe flow model can be further improved regarding post-pore stability by utilizing specific post-bore oscillation suppression techniques, and it can be integrated into a practical hydraulic modeling tool for pipeline networks in future work.

Assessment of Multigrid Schemes with Fixed Patterns for a Two-Dimensional Heat Transfer Problem

Heat transfer problems and their solutions are of critical importance in almost all areas of engineering and technology, while many real-world problems are inherently three-dimensional. Simplifying them to 2D models offers practical advantages with reasonable models. With being the fundamental class of problem of heat transfer, the 2D thermal diffusion problem was selected for the study. Multigrid methods were referred to as standing out in terms of cost reduction while keeping solution accuracy. The effectiveness of multigrid methods employing fixed pattern schemes was subject to investigation. To set up numerical experimentation, an authentic code generation effort was given that implements a basic finite volume method, intergrid operations and iterative solvers. A reference case with an analytical Laplace solution was selected and properly validated by the results. A variety of multigrid schemes with fixed patterns were explored around parameters, iterations per sweep and maximum coarsening level. Results were compiled on the focal points of cost and performance. A comparison of the direct iterative methods with multigrid schemes proved the effectiveness of multigrid schemes. With the assessment of the cost and performance outcomes, it is concluded that any multigrid scheme should visit the maximum coarsest level possible while keeping a minimum number of iterations on each grid resolution.

Direct hydroacoustics analyses of pipe orifice using lattice Boltzmann method

Acoustic waves in water pipes pose a structural threat but also offer a valuable tool for non-invasive inspection. Complex pipe geometries such as bends and surface liners create complex fluid boundaries, triggering interactions between fluid flow and acoustics. The lattice Boltzmann method (LBM) excels at capturing these interactions near complex boundaries, in contrast to the finite volume method, which can result in errors. However, the application of LBM in water pipes has been limited by stability problems. This study proposes a two-step (DM-TS) collision operator based on a direct method (LBM-HA) for stable LBM simulations in water pipes. LBM-HA enables direct hydroacoustic predictions for both acoustic and dynamic flow fields in a pipe orifice. A novel acoustic-dynamic complex boundary condition was formulated from the linearized Euler's equation to account for the physical effects of the bounded domain of the LBM-HA analysis. To distinguish between dynamic and acoustic components, wavenumber and frequency decomposition techniques were applied to the pressure data obtained within the pipe. In addition, mode decomposition of the acoustic pressure was conducted to identify the dominant acoustic modes. By comparing the LBM-HA results with experimental data, we highlighted the method's potential for direct hydroacoustic analysis considering the acoustic characteristics of the water pipe.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Direct numerical simulation of coalescence and separation of binary droplet collision with lamella stabilization

Binary droplet collision is a fundamental aspect of various natural phenomena and industrial applications. In this work, direct numerical simulation of coalescence and separation of binary droplet collision is performed over a wide range of Weber numbers and impact factors. The incompressible Navier–Stokes equations are solved by the finite volume approach, coupled with the volume of fluid method. To address the inaccurate prediction of thin lamella in simulation, a lamella stabilization method is introduced to resolve the lamella by adjusting the grid resolution. Compared with experimental data, it is validated that the lamella can be accurately and fully captured with this lamella stabilization method. Moreover, the analysis of shape and energy during the collision is conducted, and the variation of lamella is described in detail, particularly the evolution of the thickness of lamella. The results suggest that for obtaining the full variation of lamella, the maximum refinement size of the grid can reach D/4096. It is also found that without lamella stabilization, excessive dissipation can lead to the failure of predicting coalescence and separation, especially for the cases in the transition between coalescence and separation. Furthermore, even if the same collision outcome can be obtained without lamella stabilization, the number and size of droplets have obvious differences.

Overlapping domain decomposition methods for finite volume discretizations

Two-level additive overlapping domain decomposition methods are applied to solve the linear system arising from the cell-centered finite volume discretization methods (FVMs) for the elliptic problems. The conjugate gradient (CG) methods are used to accelerate the convergence. To analyze the preconditioned CG algorithm, a discrete L2 norm, an H1 norm, and an H1 semi-norm are introduced to connect the matrices resulting from the FVMs and related bilinear forms. It has been proved that, with a small overlap, the condition number of the preconditioned systems does not depend on the number of the subdomains. The result is similar to that for the conforming finite element. Numerical experiments confirm the theory.

A Study on the Effectiveness of Climate Adaptation Materials for Urban Heat Islands using Digital Twin and Computational Fluid Dynamics

This study analyzed the impact of climate adaptation materials on the mitigation of urban heat islands (UHI) using digital twin visualization and computational fluid dynamics (CFD) technology. The effects of UHI due to increased impervious surfaces have become more pronounced, and climate-adaptation materials are gaining attention as potential solutions. In this study, the impact of climate adaptation materials on UHI mitigation was analyzed using the CFD program STAR-CCM+ based on the finite volume method (FVM). The selected research site was Byeoryang-dong, Gwacheon City, and four simulation scenarios were created based on the emissivity values of the asphalt and concrete materials. The results showed that application of climate adaptation materials decreased the surface and aboveground (1.5 m) temperatures by 6.3 and 0.8 °C, respectively. This study suggests that climate adaptation materials can significantly mitigate UHI.

Multi-Objective Numerical Analysis of Horizontal Rectilinear Earth–Air Heat Exchangers with Elliptical Cross Section Using Constructal Design and TOPSIS

This study presents a numerical evaluation of a Horizontal Rectilinear Earth–air Heat Exchanger (EAHE), considering the climatic and soil conditions of Viamão, Brazil, a subtropical region. The Constructal Design method, combined with the Exhaustive Search, was utilized to define the system constraints, degree of freedom, and performance indicators. The degree of freedom was characterized by the aspect ratio between the vertical and horizontal lengths of the elliptical cross-section duct (H/L). The performance indicators for the EAHE configurations were assessed based on thermal potential (TP) and pressure drop (PD). The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was applied for multi-objective evaluation, and a methodology for EAHE is proposed. The problem was solved using FLUENT software (version 2024 R2), which employs the Finite Volume Method to solve the conservation equations for mass, momentum, and energy. The (H/L)T,o = 6.0 configuration showed a 16.4% increase in thermal performance for heating and 15.9% for cooling compared to the conventional circular duct. Conversely, the (H/L)F,o = 1.0 configuration reduced pressure loss by 65.33%. The integration of Constructal Design with TOPSIS facilitated the identification of optimized geometries that achieve a balance between performance indicators and those that specifically prioritize thermal or fluid dynamic aspects, being this approach an original scientific contribution of the present work.

An Elastohydrodynamic model of the slot-die coating process

Abstract The slot-die coating process plays an important role in the industry, as it is employed in many different fields. The characteristics of the final application are determined by the flow between the die and the roller. This research paper aims to develop a mathematical model of such flow that takes into account the roller deformations caused by high pressure values reached by the coating fluid. This Elastohydrodynamic model is made up of a coupling between the mathematical model of the flow and the mathematical model of the roller deformations. Model resolution is undertaken numerically by deforming the flow domain according to the roller deformations using computational fluid dynamics (CFD) and computational solid mechanics (CSM) techniques. For its part, the finite volume method (FVM) is used to perform the flow model analysis while the finite element method (FEM) is employed to deal with roller deformations. The results obtained from this model give information on the flow pressure distribution, coating gaps, meniscus position, extent of roller deformations in the coating flow and the influence of different operating conditions. The information obtained from this study is valuable for industrial applications, as it gives insights into the coating process that can help manufacturers to define a suitable combination of operating parameters in order to obtain coating applications that meet quality and performance requirements.

Numerical Simulation of the Hysteresis Phenomenon and Asymmetrical Configuration of Turbulent Gas Flow in an Over-Expanded Nozzle Flows

The turbulent flow within Over-Expanded Nozzles is characterized by shock waves inducing unsteady separation of the boundary layer, which can exhibit both free and restricted detachment. This study investigates various physical phenomena encountered during the expansion regime, including supersonic jet formation, jet separation, adverse pressure gradients, shockwave interactions, turbulent boundary layers, compressible mixture layers, and large-scale turbulence. These complex phenomena significantly influence nozzle performance. Utilizing numerical simulations based on the resolution of Navier-Stokes equations via finite volume methods and employing the CFD-FASTRAN code, this research analyzes detachment characteristics, transition phenomena, and the predictive accuracy of different turbulence models. A test case from the ATAC project CNES-ONERA (Aerodynamics of Hoses and Back-bodies), is examined to elucidate the hysteresis phenomenon and asymmetrical configurations resulting from boundary layer detachment.

Cosmological Radiation Simulation Analysis: Taking Arepo-RT as an Example

With the fast-growing progress in computational physics, astrophysical simulations are made possible and continually upgraded with novel physical models. Contemporarily, many modern simulations feature the capability of cosmological radiation. In order to collate the recent improvements in this field, the numerical solver Arepo-RT is discussed as an important example. This study reorganizes and interprets the main physical models and numerical techniques used in Arepo-RT and similar solvers, with some details simplified to suit common readers. This paper describes simply and briefly the finite volume method, the radiative transfer model, the radiation source model, the Godunov-type schemes and the time integration, all of which are frequently used in modern radiation simulations. Apart from the realizations of the solvers, the results and limitations are also outlined in this paper, including the justification of reduced speed of light approximation, the results compared with JWST, and the issue of missing photons. These results shed light on guiding further improvements for Arepo-RT.

Impacts of geometric factors on the hydrothermal characteristics in a shell and cone-shaped coil heat exchanger

Cone coils have a larger surface area and produce more turbulence, which enhances the heat exchange rate, making them a more efficient option for improved heat transfer than simple coils in shell-and-coil heat exchangers. In addition to reducing fouling and the requirement for maintenance, the cone shape may also provide the benefit of a self-cleaning action. Ensuring a more even flow distribution maximizes the heat exchanger's surface area use and reduces poor-flow zones. Applications needing compact solutions without compromising performance significantly benefit from this design's versatility, allowing customization to meet unique operational demands. This work evaluates numerically the impact of employing a cone-shaped coil tube in a shell-and-coil tube heat exchanger, considering various configurations and coil pitches. A commercial CFD code is used to perform the numerical simulations based on the finite volume approach. The present study has two sections. In the first part, three different coil configurations were considered. The best case was considered according to the numerical results obtained from the first section. Then, in the second part, the impact of the cone coil pitch on the hydrothermal characteristics was analyzed. The obtained numerical outcomes revealed that the best performance evaluation criteria factor belongs to the cone-shaped coil with divergent configuration by about 64.1 % and 57.45 % more than the cone-shaped coil with convergent configuration at De = 1,000 and De = 2,500, respectively. Moreover, the cone-shaped coil with a divergent configuration displayed higher JF values by approximately 61.54 % and 58.06 % than a cone-shaped coil with a convergent configuration at De = 1,000 and De = 2,500, respectively. Among different evaluated cone coil pitches, the maximum performance evaluation criteria factor belongs to the case with pitch values of 40 mm. Moreover, the JF value increases by approximately 4.76 % and 5.56 %, respectively, at De = 1,000, when the pitch value grows by around 60 % and 100 %. Furthermore, when the pitch value climbs by 60 % and 100 %, at De = 2,500, the JF value rises by roughly 12.16 % and 19.59 %, respectively.

A finite discrete element approach for modeling of desiccation fracturing around underground openings in Opalinus clay

Understanding and predicting potential failure mechanisms during the excavation and open drift stages of geological repository construction are among the crucial aspects of performance evaluation and safety assessment of nuclear waste storage facilities. The development of the Excavation Damage Zone (EDZ) and the generation of shrinkage-induced cracks during operational phases are prominent examples of failure mechanisms that can compromise the integrity of the repository systems. This study presents an integrated framework for investigating shrinkage-induced cracking of Opalinus Clay in niches and tunnels. To achieve this, the hybrid Finite Discrete Element Method (FDEM) is employed. The methodology incorporates a two-way staggered hydro-mechanical coupling scheme, where solid phase analysis relies on 2D FDEM and fluid flow is modeled using the nonlinear Richards’ equation and solved via Finite Volume discretization. To account for the effects of EDZ, characterized by a pronounced increase in hydraulic conductivity, a numerical simulation of tunnel excavation is first carried out. The resulting failure pattern around underground openings is then abstracted through the definition of an altered hydraulic conductivity field. Comparison of the numerical results with field observations demonstrates the framework’s ability to capture a wide range of failure mechanisms inherent in various stages of underground repository construction in Opalinus Clay.

Computational analysis of pulsatile blood flow and heat transport dynamics in middle cerebral artery aneurysms in different body physiologies

This paper presents a comprehensive hemodynamic evaluation of two endovascular techniques for treating cerebral aneurysms. Using the finite volume method, we simulated pulsatile blood flow and heat transport dynamics in two saccular aneurysms of varying sizes and shapes. We assessed hemodynamic factors under two coiling conditions with different porosities and deformation stages to identify the most effective treatment for each case. Our computational analysis reveals that stent and coiling applications are more efficient for aneurysms with low-sac volume. Notably, stent placement proves to be more effective than coiling in treating saccular aneurysms. Our findings indicate that stent-induced deformation sufficiently diverts the main blood flow, thereby reducing the risk of aneurysm rupture near the ostium region.