Finite Volume Research Articles

Potential effects of internal dam-break in Stare Miasto Reservoir in Poland

Study regionThe research object is located in Wielkopolska province (Poland), which is well-known for its rural character and scarcity of water. To prevent droughts, small reservoirs are installed in local watersheds. It enables control of water conditions for agriculture and improvement of local climate. The main challenge is prevention from the deposition of sediments in a reservoir. To minimize this threat, the specific constructions of the reservoir are applied, e.g. internal dams. Study focusThe Stare Miasto reservoir consists of an internal dam with the upper zone separated. The highway bridge split the main part. In 2014 a flood wave propagated through the reservoir. The crest of the internal dam was shifted generating a potential risk of internal dam failure. The consequences of such an event were analyzed using a two-dimensional hydrodynamic numerical tool that solves the shallow water equations with finite volume method on unstructured mesh. New hydrological insight for the regionThe results obtained prove that the dam break increases the risk of bridge instability. The shear stresses generated during break of internal dam may exceed 50 N/m2, what cause danger of deep scour generation under and below the construction. Unexpectedly, the existence of the bridge decreased the threat of the main dam overtopping. The study may be a valuable inspiration for the design of new reservoirs inevitable in controlling water resource conditions in the region.

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

Energy-Preserving Hybrid Asymptotic Augmented Finite Volume Methods for Nonlinear Degenerate Wave Equations

Energy-Preserving Hybrid Asymptotic Augmented Finite Volume Methods for Nonlinear Degenerate Wave Equations

Convergence of the Finite Volume Method for Stochastic Hyperbolic Scalar Conservation Laws: A Proof By Truncation on the Sample-Time Space

Convergence of the Finite Volume Method for Stochastic Hyperbolic Scalar Conservation Laws: A Proof By Truncation on the Sample-Time Space

New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws

New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws

The Positivity-Preserving Finite Volume Coupled with Finite Element Method for the Keller–Segel–Navier–Stokes Model

The Positivity-Preserving Finite Volume Coupled with Finite Element Method for the Keller–Segel–Navier–Stokes Model

A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme

A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme

Multifaceted simulation: Finite volume and finite element modeling of blood flow in multiple stenosed arteries

Cardiovascular illnesses are a primary global health concern because they are frequently brought on by arterial stenosis. The complicated hemodynamics of blood flow via elliptically shaped arteries with numerous stenotic lesions along their top and bottom walls are examined in this paper. Carreau fluid model is used with Navier–Stokes equations in this study. The complete comparative study is done by using the Finite Element and Finite Volume Methods. This study uses commercial software to examine blood flow velocity, pressure and temperature distributions under various physiological situations at Reynolds number 30. Our results illuminate the interaction between flow dynamics, stenosis characteristics, and arterial geometry. The novelty of the work is to investigate how stenosis size, shape, and location affect pressure gradients, and flow disturbances. These observations provide helpful direction for understanding disease progression, designing treatments, and possibly new stent designs. The future direction of this research may involve further exploration of the interplay between hemodynamics and arterial stenosis by incorporating advanced computational models. Additionally, studies focusing on in vivo validation and clinical applications could enhance the translational impact of the findings. Collaborations between researchers, clinicians, and engineers may pave the way for personalized treatment strategies and innovations in cardiovascular care based on a deeper understanding of the intricate dynamics within diseased arteries.

Gauge Field Marginal of an Abelian Higgs Model

We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on arbitrary finite graphs and does not assume that the structure group is Abelian, is a loop expansion of the Radon–Nikodym derivative of the law of the gauge field marginal with respect to that of the pure gauge theory. This expansion is similar to the one of Seiler (Gauge theories as a problem of constructive quantum field theory and statistical mechanics, volume 159 of lecture notes in physics, Springer, Berlin, p v+192. https://doi.org/10.1007/3-540-11559-5, 1982) but holds in greater generality and uses a different graph theoretic approach. Furthermore, we show ultraviolet stability for the gauge field marginal of the model in a fixed gauge. More specifically, we show that moments of the Hölder–Besov-type norms introduced in Chevyrev (Commun Math Phys 372(3):1027–1058. https://doi.org/10.1007/s00220-019-03567-5, 2019) are bounded uniformly in the lattice spacing. This latter result relies on a quantitative diamagnetic inequality that in turn follows from the loop expansion and elementary properties of Gaussian random variables.

Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system

Abstract In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we apply the penalty approach to control domain-related discretization errors. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

Experimental test and analysis of impact suppression for hydraulic-driven leg using a new MR damper with multi-channels

When hydraulic-legged robots move under high loads on irregular ground, they are vulnerable to ground impacts. Vibration affects the motion performance of the robot and damages its mechanical structure. This study aims to improve the properties of vibration absorption and impact resistance of hydraulic-legged robots. Because the traditional MR damper (MRD) has small output in finite volume, a novel MRD with a multistage flow channel (MFC-MRD) can output a large damping force designed. First, an MRD prototype was designed for a mechanical leg’s driving joint. Subsequently, the system is analyzed theoretically, and a semi-active control strategy is designed and simulated. Finally, the vibration and impact resistance of the prototype were tested. The experimental results show that in the signal tracking experiment, the maximum overshoot under semi-active control was reduced by 53.0%, and the settling time was reduced by 76.9% compared with the passive control. The impact test reduced the maximum displacement fluctuation by 41.09%, and the buffer time is only 0.24 s.

A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows

AbstractThis paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows, interacting with moving solid obstacles. A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase, a solid phase, and the surrounding void. According to the so-called diffuse interface approach, the different phases and consequently the void are described by means of a scalar volume fraction function for each phase. In our numerical scheme, the dynamics of the liquid phase and the motion of the solid are decoupled. The solid is assumed to be a moving rigid body, whose motion is prescribed. Only after the advection of the solid volume fraction, the dynamics of the liquid phase is considered. As usual in semi-implicit schemes, we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly, while the pressure terms are treated implicitly. The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach. The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique. The time step size is only limited by the velocities of the two phases contained in the domain, and not by the gravity wave speed nor by the stiff algebraic relaxation source term, which requires an implicit discretization. The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.

Modeling heat and mass transfer in metal hydride hydrogen storage systems: Impact of operating parameters and reactor geometry

This work introduces a transient 2D axis-symmetrical model for hydrogen absorption in a cylindrical LaNi5 reactor employing finite volume method with a fully implicit Euler's time integration scheme, coupling equations for heat, mass, and momentum transport. The validated model is used to investigate the impacts of pressure, cooling fluid temperature, and variations in reactor geometry and size on temperature and reacted fraction profiles. The findings reveal that the charging pressure affects both peak temperature and reaction kinetics, whereas cooling fluid temperature predominantly impacts the absorption kinetics. A comparative analysis of two models, one incorporating Darcy's velocity and one without, demonstrates that while Darcy's law introduces numerical instability in the coupled equations, its impact on the model outcomes is negligible. The effect of changing the non-homogeneous Neumann to Dirichlet boundary condition is also demonstrated to anticipate the utilization of phase change materials (PCM) instead of the cooling fluid.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Assessment of heat transfer capabilities of some known nanofluids under turbulent flow conditions in a five-turn spiral pipe flow

Abstract In this study, the thermo-flow behaviours of the spiral tube were examined using water and some nanofluids such as TiO2, Al2O3, Fe2O3, CuO, ZnO, and CeO2. The computational flow dynamic modelling of the spiral coiled tube was performed with ANSYS 20 software program. The k–ε model with a standard wall function was used to simulate the thermo-flow characteristics. The solution of the governing equations was performed using the discretization method of finite volume. The study was carried out considering the case of fluid-to-fluid heat transfer in turbulent conditions. The influence of different key design parameters such as Reynolds number, different nanofluids, and flow arrangements was of main interest. The volume concentration of the nanofluids is 1%. The experiments were performed at different Reynolds ranges (9,000, 14,000, 20,000, and 25,000). The outlet temperature values, heat transfer coefficient, coefficient of friction, Nusselt number values of water, and nanofluids were found and compared. It was found that the outlet temperature, heat transfer coefficient, and Nusselt number values of water were the lowest, while the coefficient of friction value was the highest compared to the nanofluids. Among the nanofluids, CeO was found to have the highest outlet temperature, heat transfer coefficient, and Nusselt number value, as well as the lowest coefficient of friction value. TiO2 was found to have the lowest outlet temperature (T out), the heat transfer coefficient value, and the highest coefficient of friction value. Al2O3 was found to have the lowest Nusselt number. In addition, Nusselt number values were obtained at different Dean numbers of water (2,200, 3,400, 4,900, 6,100, 7,350, and 8,600) and found to be compatible with previous studies. In addition, the coefficients of friction values of water at different velocities (0.18, 0.24, 0.41, 0.71, 0.95, 1.07, and 1.18) were obtained and found to be compatible with previous studies.

Block Spectral Method Analysis for Turbomachinery Applications

Abstract The block-wise spectral reconstruction of turbomachinery flows has been successfully used in the past to reduce the computational cost of full-annulus turbomachinery simulations. The rationale of the method is based on an explicit representation of the long-wavelengths of the problem using a Fourier expansion of the blocks, which in turn contain the short-wavelength content of the spectrum. This work analyzes the accuracy of this approach and shows that this approximation retains not only the explicit Fourier representation of the long wavelengths and finite volume approximation of the short wavelengths but their interaction as well. This interaction due to the scattering associated with the nonuniformity of the flow is referred to as Tyler–Sofrin modes by turbomachinery practitioners and is highly relevant for many practical applications. The solution’s harmonic content is illustrated by resorting to the linear wave equation with varying propagation speed and the NASA rotor 67 fan.

Response of salt intrusion in a tidal estuary to regional climatic forcing

Abstract Salinity distribution in a large tidal estuary is subject to estuarine adjustment under the influences of multiple physical drivers such as freshwater pulses and sea level rise, and is crucial to upstream water quality, aquaculture, and ecosystem functions of the estuary. To better understand the estuarine salinity response to climate change, the unstructured-grid Finite Volume Community Ocean Model was implemented to simulate the salt intrusion in the Delaware Bay Estuary. The model was first validated by multiple observational data sets and subsequently applied in an idealized setting to examine the response of salt front to freshwater pulses in high flow conditions, followed by a long-term drought condition supported by a multi-decadal streamflow drought analysis in the estuary. The model results showed that after the freshwater pulses the salt front location moved further upstream with sea level rise. Under the simulated long-term drought condition, the adjustment timescale of salt intrusion varies nonlinearly with sea level rise. With a significant increase in sea level rise, the adjustment timescale starts to decrease. This shift suggests a transition into a different regime where the estuary becomes more stratified, as indicated by an increasing bulk Simpson number with rising sea levels.

Analysis of nonlinear problems using the Dual Mesh Control Domain Method with arbitrary meshes

The Dual Mesh Control Domain Method (DMCDM), proposed and developed by the second author, is a recent advancement in the field of numerical methods. This method represents a blend of the Finite Element Method (FEM) and the Finite Volume Method (FVM), each having its primary domains of popularity. The DMCDM incorporates the concepts of interpolation, duality, and numerical integration from the former and the idea of satisfying the integral (global) form of the differential (or balance) equations from the latter. In this paper, we present a fresh and systematic approach to solving two-dimensional nonlinear problems, including advection–diffusion problems, with arbitrary primal meshes. We develop an approach where element-level equations are derived and assembled in a manner similar to that of the FEM, as opposed to using nodal equations, as has been the convention in all of the previous works involving the DMCDM. Additionally, we extend the previous works to include higher-order interpolation, specifically quadratic interpolation. In short, we provide formulations for four-node bilinear and nine-node biquadratic elements of quadrilateral shape, enabling the application of the DMCDM to arbitrary primal and dual meshes. Finally, we explore the Newton iteration method for linearizing the nonlinear system of equations that arises from the DMCDM discretization. We present numerical results and comparisons against available exact and numerical solutions to verify the accuracy and robustness of the DMCDM.

Efficient WENO Schemes for Nonuniform Grids

A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.