FV Method Research Articles

Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration

This article aims at presenting a new local subcell monolithic Discontinuous-Galerkin/Finite-Volume (DG/FV) convex property preserving scheme solving system of conservation laws on 2D unstructured grids. This is known that DG method needs some sort of nonlinear limiting to avoid spurious oscillations or nonlinear instabilities which may lead to the crash of the code. The main idea motivating the present work is to improve the robustness of DG schemes, while preserving as much as possible its high accuracy and very precise subcell resolution. To do so, a convex blending of high-order DG and first-order FV schemes will be locally performed, at the subcell scale, where it is needed. To this end, by means of the theory developed in [58,59], we first recall that it is possible to rewrite DG scheme as a subcell FV method, defined on a subgrid, provided with some specific numerical fluxes referred to as DG reconstructed fluxes. Then, the subcell monolithic DG/FV method will be defined as follows: to each face of each subcell we will assign two fluxes, a 1st-order FV one and a high-order reconstructed one, that in the end will be blended in a convex way. The goal is then to determine, through analysis, optimal blending coefficients to achieve the desired properties. Numerical results on various type problems will be presented to assess the very good performance of the design method.A particular emphasis will be put on entropy consideration. By means of this subcell monolithic framework, we will attempt to address the following questions: is this possible through this monolithic framework to ensure any entropy stability? What do we mean by entropy stability? What is the cost of such constraints? Is this absolutely needed while aiming for high-order accuracy?

A face-centred finite volume method for laminar and turbulent incompressible flows

This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the negative Spalart–Allmaras (SA) model and three novel convective stabilisations, inspired by Riemann solvers, are derived and compared numerically. The resulting method achieves first-order convergence of the velocity, the velocity-gradient tensor and the pressure. FCFV accurately predicts engineering quantities of interest, such as drag and lift, on unstructured meshes and, by avoiding gradient reconstruction, the method is less sensitive to mesh quality than other FV methods, even in the presence of highly distorted and stretched cells. A monolithic and a staggered solution strategies for the RANS-SA system are derived and compared numerically. Numerical benchmarks, involving laminar and turbulent, steady and transient cases are used to assess the performance, accuracy and robustness of the proposed FCFV method.

A non-intrusive data-driven reduced order model for parametrized CFD-DEM numerical simulations

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations needs to be studied. In this context, we develop a non-intrusive data-driven reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The main novelties of the proposed approach rely in (i) the combination of ROM and FV methods, (ii) a numerical sensitivity analysis of the ROM accuracy with respect to the number of POD modes and to the cardinality of the training set and (iii) a parametric study with respect to the Stokes number. We test our ROM on the fluidized bed benchmark problem. The accuracy of the ROM is assessed against results obtained with the FOM both for Eulerian (the fluid volume fraction) and Lagrangian (position and velocity of the particles) quantities. We also discuss the efficiency of our ROM approach.

Assessing The Key Physical Capabilities in Striking Combat Sports: Reliability And Reproducibility of A New Test

The rules and the technical aspect of combat sports make it difficult to determine key performance indicators. Therefore, the assessment of striking sports discipline-specific key components may be relevant. This study aims to present a test assessing specifically the fighters striking force-velocity (F-V) capabilities. 10 MMA fighters performed FV (two-point (TP) and multiple-point (MP) methods) and fatigue tests using the landmine punch exercise (LPE) which is considered a specific exercise for striking combat sports. A high within-subject intra-session and inter-session reliability and reproducibility were found for the FV profiles parameters and the fatigue test (most CVs<10%, ICCs>0.67, ES < 0.2 for F0, V0, Pmax, Sfv, Ppeak, Pmean, Pmin and FI% and r > 0.9). Moreover, the TP and MP methods showed high validity and agreement (r >0.88 and ES <0.37). The novel LPE test presented in this pilot study is a highly reproducible tool for evaluating both mechanical and anaerobic components specific to the discipline. Athletes and coaches may use this test to better understand striking performance in combat sports.

Urban tree risk assessment

Urban trees provide ecosystem services of great importance to the city. To take advantage of these services, it is important that the trees are in good condition, minimizing the risk to people, goods, and essential activities due to the fall of branches or entire trees. Therefore, their condition must be duly evaluated to favor their presence in the city with acceptable levels of risk. The main goal of the research was to propose a visual risk assessment protocol for urban trees located in parks in Montevideo, Uruguay. The methodology was divided into three phases, carried out between October 2018 and February 2021 at Parque José Batlle y Ordóñez. A total of 60 trees were assessed, 30 of the Tipuana genus and 30 of Eucalyptus, with 17 assessors of different levels of knowledge and experience participating. In phase 1, the three levels of risk assessment were analyzed, according to the ANSI A300 standard (limited, basic, and advanced), six methods of basic visual assessment used internationally, and non-destructive evaluations (sonic tomography and resistograph). In phase 2, three evaluation methods were developed and analyzed (Fast Visual - FV, Basic Visual - BV and Detailed Visual - DV). In phase 3, a risk assessment protocol with these three levels was built and analyzed. The main findings showed significant differences between types of assessors, genus, methods, and interaction between them. The proposed FV, BV and DV evaluation methods were effective and efficient in the applied situations. The semi-quantitative risk rating analysis proved to be more suitable for the BV method, while the qualitative analysis was more suitable for the DV. Good repeatability of the use of the protocol was observed, with an average agreement of 80% in FV and DV methods and 60% in BV. The proposed protocol was able to discriminate trees by their level of risk and is viable to be used in urban parks in Montevideo.

Error estimate of the non-intrusive reduced basis method with finite volume schemes

The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce computational costs of a classical high fidelity code based on Finite Element Method (FEM), Finite Volume (FVM) or Spectral methods. The efficient implementation of most of these RBM requires to modify this high fidelity code, which cannot be done, for example in an industrial context if the high fidelity code is only accessible as a "black-box" solver. The Non-Intrusive Reduced Basis (NIRB) method has been introduced in the context of finite elements as a good alternative to reduce the implementation costs of these parameter-dependent problems. The method is efficient in other contexts than the FEM one, like with finite volume schemes, which are more often used in an industrial environment. In this case, some adaptations need to be done as the degrees of freedom in FV methods have different meanings. At this time, error estimates have only been studied with FEM solvers. In this paper, we present a generalisation of the NIRB method to Finite Volume schemes and we show that estimates established for FEM solvers also hold in the FVM setting. We first prove our results for the hybrid-Mimetic Finite Difference method (hMFD), which is part the Hybrid Mixed Mimetic methods (HMM) family. Then, we explain how these results apply more generally to other FV schemes. Some of them are specified, such as the Two Point Flux Approximation (TPFA).

Numerical simulation of temperature histories of frozen minced meat having different fat contents during ohmic thawing

The ohmic thawing (OT) of minced meat sample was mathematically modelled using different numerical methods (Finite Difference-FD and Finite Volume-FV) for different process conditions (voltage gradients of 10, 13 and 16 V/cm and fat contents of meat sample as 2%, 10% and 18%). FD method was successful to predict the temperature changes for both heating and phase change regions. FV method was performed by using two different heat generation functions; depending on process time (UDF-1) or the center temperature (UDF-2). The description of the change of heat generation term depending on process time (UDF-1) in the ANSYS module was more successful with the experimental data compared to the description of the change of heat generation term depending the center temperature (UDF-2). Although FV model is more complex than FD model it can be applied for simulation of detailed temperature distributions. On the other hand, FD model can be applied for practical predictions of temperature histories for center temperatures in simple geometries. It is thought that the simulation of OT performed at different conditions with the FD and the FV methods would contribute valuable data in the design of household ohmic thawing/cooking systems for solid food materials.

Customised weight-based volume contrast media protocol in CT of chest, abdomen and pelvis examination

IntroductionFixed volume (FV) contrast media administration during CT examination is the standard practice in most healthcare institutions. We aim to validate a customised weight-based volume (WBV) method and compare it to the conventional FV methods, introduced in a regional setting. Methods220 patients underwent CT of the chest, abdomen and pelvis (CAP) using a standard FV protocol, and subsequently, a customised 1.0 mL/kg WBV protocol within one year. Both image sets were assessed for contrast enhancement using CT attenuation at selected regions-of-interest (ROIs). The visual image quality was evaluated by three radiologists using a 4-point Likert scale. Quantitative CT attenuation was correlated with the visual quality assessment to determine the HU's enhancement indicative of the image quality grades. Contrast media usage was calculated to estimate cost-savings from both protocols. ResultsMean patient age was 61 ± 14 years, and weight was 56.1 ± 8.7 kg. FV protocol produced higher contrast enhancement than WBV, p < 0.001. CT images' overall contrast enhancement was negatively correlated with body weight for FV protocol while the WBV protocol produced more consistent enhancement across different body weight. More than 90% of the images from both protocols were graded “Excellent”. WBV protocol also enabled a 28% cost reduction with cost savings of US$1238. ConclusionThe customised WBV protocol produced CT images which were comparable to FV protocol for CT CAP examinations. A median CT value of 100 HU can be an indicator of good image quality for the WBV protocol.

Naked‐Eye Readout of Analyte‐Induced NIR Fluorescence Responses by an Initiation–Input–Transduction Nanoplatform

AbstractFluorescence visualization (FV) in the near‐infrared (NIR) window promises to break through the signal‐to‐background ratio (SBR) bottleneck of traditional visible‐light‐driven FV methods. However, straightforward NIR‐FV has not been realized, owing to the lack of methods to readily transduce NIR responses into instrument‐free, naked eye‐recognizable outputs. Now, an initiation–input–transduction platform comprising a well‐designed NIR fluorophore as the signal initiator and lanthanide‐doped nanocrystals as the transducer for facile NIR‐FV is presented. The analyte‐induced off–on NIR signal serves as a sensitizing switch of transducer visible luminescence for naked‐eye readout. The design is demonstrated for portable, quantitative detection of phosgene with significantly improved SBR and sensitivity. By further exploration of initiators, this strategy holds promise to create advanced NIR‐FV probes for broad sensing applications.

Numerical simulations of magnetorheological fluids flowing between two fixed parallel plates

• A magnetorheological fluid has been computed with the FV method in a collocated grid. • Computing the magnetic induction field is fundamental for obtaining accurate results. • Some recirculation zones at the magnetic-nonmagnetic interfaces were found that showed some discrepancies with other authors. In this paper, a study on the motion of a magnetorheological fluid (MRF) under application of a magnetic external field is presented. The magnetic field is perpendicular to two non-conducting flat parallel plates which are stationary. Numerical simulations are provided by an in-house CFD code developed by the authors and adapted to include the magnetohydrodynamics (MHD) field equations. Solutions studied show how these magnetic fields can modify both the velocity profile and the pressure drop along the channel. Numerical solutions are firstly compared with analytical ones in some simple cases in order to verify the computational code. Relative errors remained around 10 − 4 . A second test was set up where a magnetic field is applied only in a portion of the channel in order to control the flowrate . The results showed that with strong magnetic fields , the flowrate could be reduced up to 90% from a normal state, i.e. B = 0 T. The maximum velocity at the centreline shows a peak at the outlet of the region where the magnetic field is applied due to the acceleration of the fluid when the magnetic forces disappear. When employing the code in a geometry similar to that presented in a previous paper in which the authors used a commercial code, some discrepancies were found, especially at the edges of the zone where the magnetic field was applied. Some speculations about this disagreement are put forward.

Management of Natural Ventilation in High-Rise Building – a CFD Study

The natural ventilation of a 7 floors office building was studied in terms of its openings’ discharge coefficient. A 2D, steady state, incompressible CFD model was developed using the FV method. The developed CFD model was validated against experimental data from wind tunnel measurements. Discharge coefficient is calculated for three elevations (ground floor, 4th and 7th floor) considering four combination of inclination angles 15o and 30o for windward and leeward openings. It was examined the dependence of discharge coefficient from: the wind velocity, the characteristics of the field where the building is situated (roughness length and atmospheric boundary layer thickness) considering four field types: a) Urban area (center and suburbs), b) Open field (classes 2 and 3). Two types of discharge coefficient was calculated, one based on the wind velocity at the opening, Cd, and one based on the wind velocity at the infinity, Cdw. The first varies between 0.54 to 0.7 but the second varies between 0.13 to 0.89 and it is considered more usable since it relates the buildings’ ventilation to the average wind velocity in the examined area, information available to the designer. Both are depended on the openings’ inclination angle, from the elevation of the examined floor, from the field roughness length around the building and from the wind turbulence intensity.

H&lt;sup&gt;1&lt;/sup&gt;-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

H&lt;sup&gt;1&lt;/sup&gt;-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations

AbstractA concept of “static reconstruction” and “dynamic reconstruction” was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a “hybrid reconstruction” approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piece-wise polynomial are computed locally in a cell by the traditional DG method (called as “dynamic reconstruction”), while the higher-order derivatives are re-constructed by the “static reconstruction” of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

AbstractWe have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix‐free implicit cell‐centered FV method. The pressure Poisson equation is solved by the node‐based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered‐mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix‐free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid. Copyright © 2009 John Wiley &amp; Sons, Ltd.

On the characteristics-based ACM for incompressible flows

In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475–484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667–685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466–1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309–325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657–663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584–607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5–7) (2000) 733–756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5–7) (2000) 733–756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.

Cardiac Output Measured by a New Arterial Pressure Waveform Analysis Method Without Calibration Compared With Thermodilution After Cardiac Surgery

To investigate whether measuring cardiac output and its course after cardiac surgery by a new analysis technique of radial artery pressure waves, without need for calibration (FloTrac/Vigileo [FV]; Edwards Lifesciences, Irvine, CA), conforms to the standard bolus thermodilution method via a pulmonary artery catheter (PAC). Prospective study. Intensive care unit of university hospital. Twenty patients for up to 24 hours after cardiac surgery. Simultaneous and triplicate PAC thermodilution and FV cardiac output measurements at 1 and 3 hours after surgery and the following morning. Fifty-six simultaneous measurement sets were obtained. Mean cardiac output (PAC) ranged between 2.8 and 10.3 L/min and for the FV method between 3.3 and 8.8 L/min. The coefficient of variation for pooled measurements was 7.3% for the PAC and 3.0% for the FV method. For pooled data, the r2 was 0.55 (p < 0.001), with a bias of -0.14, precision of 1.00 L/min, and 95% limits of agreement between -2.14 and 1.87 L/min in a Bland-Altman plot. Also, the FV method tended to overestimate cardiac output when <7 L/min and increased with time, whereas mean arterial pressure increased and PAC cardiac output did not change. Changes in cardiac output correlated (r2 = 0.52, p < 0.001). The FV arterial pressure waveform analysis method is a clinically applicable method for cardiac output assessment without calibration, after cardiac surgery. It performs well at low cardiac outputs but remains sensitive to changes in vascular tone.

A positivity preserving finite element–finite volume solver for the Spalart–Allmaras turbulence model

We propose a stable numerical method preserving the positivity of the turbulent viscosity in the Spalart–Allmaras model focusing in particular on the stiffness of the source term. The goal is to apply this model for turbulent flows using an effective numerical method based on a mixed FE–FV method. A mathematical analysis of stability and positivity of the continuous and numerical models is provided. Numerical tests on the 3D boundary layer over a flat plate show the convergence and robustness of the proposed method confirming the theoretical analysis.

COMPARATIVE STUDY OF THERMAL FLOWS WITH DIFFERENT FINITE VOLUME AND LATTICE BOLTZMANN SCHEMES

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

Entropy Formulation for Parabolic Degenerate Equations with General Dirichlet Boundary Conditions and Application to the Convergence of FV Methods

This paper is devoted to the analysis and the approximation of parabolic hyperbolic degenerate problems defined on bounded domains with nonhomogeneous boundary conditions. It consists of two parts. The first part is devoted to the definition of an original notion of entropy solutions to the continuous problem, which can be adapted to define a notion of measure-valued solutions, or entropy process solutions. The uniqueness of such solutions is established. In the second part, the convergence of the finite volume method is proved. This result relies on (weak) estimates and on the theorem of uniqueness of the first part. It also entails the existence of a solution to the continuous problem.

Simulation of micro flows with moving boundaries using high-order upwind FV method on unstructured grids

Numerical methods are presented for the simulation of steady and unsteady micro gas flows with moving boundaries found in micro scale fluidic devices. Both steady and unsteady flows are calculated by using an implicit real-time discretization and a dual-time stepping scheme implemented in a high-order upwind finite-volume unstructured-grid Navier–Stokes solver. For moving boundary problems, a new dynamic mesh method has been developed which is shown to be robust in handling large mesh deformation. Micro-scale flows studied with the methods developed include flow in micro channels, unsteady flow around a micro cylinder in oscillation and transport processes in micro pumps. The simulation is based on the continuum fluid model (the compressible Navier–Stokes equations) with slip boundary conditions implemented in the context of unstructured grids as the micro flows studied are all in the slip flow regime. Results are presented to validate the methods and demonstrate their applications to the analysis and design of micro fluidic devices. The implicit dual-time stepping scheme is found to be robust and efficient in dealing with both steady and unsteady micro flows. The unstructured-grid solver proves to be very flexible in dealing with complex geometries such as micro pumps. This is the first known report on the use of finite-volume unstructured grid solver for studying micro flows based on the slip boundary condition with moving boundaries.