Order Upwind Scheme Research Articles

Total of time variation diminishing principle for conservation laws

We introduce a new principle for devising numerical schemes for conservation laws in one and multiple dimensions. The new formulation is based on the Total of Time Variation (TOTV) defined as the volume integral of the magnitude of the time derivative. For the one-dimensional scalar advection equation with a constant velocity, TOTV and the usual total variation (TV) are the same except for a constant factor. For non-linear equations and/or in multiple dimensions, TV and TOTV are different. We show that TOTV is a conserved quantity for one- and multi-dimensional scalar conservation laws with a non-linear flux function that can depend on the spatial coordinates as well. We call a numerical scheme that ensures that the discrete form of TOTV is not increasing in time a Total of Time Variation Diminishing (TOTVD) method. A TOTVD scheme is stable against catastrophic instabilities that would lead to uncontrolled growth of the time derivative. We show that the first order upwind scheme with a finite time step satisfying the usual CFL condition is TOTVD for all equations that satisfy the TOTVD property analytically. We demonstrate the difference between TV and TOTV with numerical tests.

The application of upwind meshless approximation finite volume method to the convection dominated problems on the unstructured and deformed meshes

The primary objective of this research is to develop a finite volume method that can incorporate the most widely recognized upwind schemes using meshless techniques on an unstructured mesh. The recently developed Meshless Approximation Finite Volume Method (MAFVM) is expected to provide a solution to the convection–diffusion equation with an extremely high Pélect number, regardless of the type or quality of mesh, even when dealing with highly distorted meshes. By incorporating the local compactly supported radial basis functions differential quadrature method (LCRBFDQ), a meshless approximation technique, the field variables, flux, and gradient are directly approximated using information from neighboring scattered nodes. Building upon this concept, we propose two meshless approximation approaches for computing the flux and gradient within the framework of the finite volume method. Elliptic type problem on regular mesh is solved using the proposed MAFVM by different flux computation methods. Parameters for MAFVM that provide accurate and robust results are suggested. Next standard linear and second order upwind schemes as well as the well-known total variation diminishing (TVD) methods are integrated into the proposed MAFVM, using the developed flux calculation method to solve convection–diffusion problem with very high Pélect number on standard or highly deformed mesh. Accurate and robust results can be observed which show that the current MAFVM can provide an alternative and better way to deal with strong convection problem on meshes of arbitrary types by the proposed meshless flux computation methods.

Transkritik Soğutma Çevrimlerinde Gaz Soğutucu Geometrisinin Sayısal Optimizasyonu

Traditional halocarbon – based refrigerants tend to considerably increase global warming and ozone depletion factors. Therefore, CO2 is fast becoming a key instrument as a natural refrigerant which was widely applied and attracted the consideration of the research community. The gas cooler is an important component in the CO2 transcritical refrigeration system and plays a key role in the performance due to the determination of operating pressure consequently power consumption. In this research, the performance characteristics of a CO2 gas cooler having wavy fin geometry, which is currently used in industries such as air conditioning, automotive and aviation, was determined experimentally in a calorimetric test room. The experimental results was used as benchmark data to validate the three – dimensional numerical model. Laminar model and realizable k - ɛ turbulent model were employed for analyses. Moreover, the second order upwind scheme was considered to discretize momentum and energy equations. Accordingly, a multi-objective optimization process has been performed employing Response Surface Method (RSM) to determine the optimum wavy fin geometry in CO2 transcritical refrigeration system. Four geometrical parameters namely longitudinal pitch, half transverse pitch, tube outer diameter, and fin pitch of the gas cooler were optimized. According to results, the new optimized CO2 gas cooler exhibited lesser pressure drop and higher heat transfer capacity in comparison with the tested gas cooler geometry used in the industry. It was found that the overall heat transfer coefficient enhancement is between 5.4 – 12.2 % while pressure drop decreases about 175.08 – 188.58 % for three different inlet velocities.

Heat exchanger with semi-circular tubes and mountings for effective heat transfer

Compact heat exchangers are widely being used in various devices owing to its minimized size and efficient operation. The traditionally fitted circular tubes in heat exchanger have been modified as semi-circular tubes with slit. This newly proposed design offers added tubes surface area of 63.69% for better fluid flow and heat exchange. To investigate, two dimensional, unsteady, incompressible and isothermal computational studies have been carried out. The different confinements (BR= 1.54d, 2d and 3d) and gap ratios (g = 0.07, 0.14 and 0.21)have been preferred in order to mimic confined fluid environment in compact heat exchangers over the Reynolds numbers range of 50-200. Ansys Workbench 18 has been employed in modeling, meshing and carrying out the simulations of the problem formulated. Pressure and velocity were coupled using the SIMPLE algorithm. The convective and diffusive terms in the governing equations were discretized using second order upwind and central difference scheme. The time step size was fixed as 0.005 and the simulation was run until flow maturity. Results claim that flow sheds well nearer to tubes with slit at BR 1.54, which is not happening for circular tubes at same BR. The arrangement with the minimum BR and maximum gap ratio offers best performance. Semi-circle combination separated by 0.21d offers best heat transfer with an improvement of 10.51% as compared to circular components at a blockage (BR) ratio of 1.54 and Re of 200.The concept of tube splits instead of circular tubes is more effective in dissipating heat whenever the flow shedding is deteriorating or completely eliminated. The overall performance parameter (ɛ) for tube split is highest when BR 3 and g 0.21.

An improved multiphase lattice Boltzmann flux solver with phase interface compression for incompressible multiphase flows

Numerical dissipation is ubiquitous in multiphase flow simulation. This paper introduces a phase interface compression term into the recently developed multiphase lattice Boltzmann flux solver and achieves an excellent interface maintenance. Here, the phase interface compression term only works in the interface region and is solved as the flux in finite volume discretization. At each cell interface, the interfacial compression velocity ur is determined by local reconstruction velocities of the multiphase lattice Boltzmann flux solver, which maintains the consistency of the flux evaluation. Meanwhile, the interfacial order parameter C in the phase interface compression term is obtained by the second order upwind scheme according to the interface normal direction. Numerical validation of the present model has been made by simulating the Zalesak problem, the single vortex problem, Rayleigh–Taylor instability, and bubble rising and coalescence. The obtained results indicate the validity and reliability of the present model.

Numerical study on the performance of photovoltaic thermal unit condenser with water/nanofluids as fluids medium

To fully exploit the use of water/nanofluids in the photovoltaic thermal (PVT) unit condenser and further increase renewable energy resources in energy mix, the current paper numerically studies the effect of operating water/PVT unit, Al3O2-water/PVT unit and Ag-water/PVT unit on the overall performance. In the ANSYS Fluent 18, the mathematical equations related to these models were discretized by the second order upwind scheme and solved at steady state, considering the fluid inside pipe as laminar flow. The results were obtained and discussed in terms of coefficient of performance (COP), Nusselt number (Nu), specific exergy (Ein,out) and outlet flow temperature (Tout), at different nanoparticle fractions and operating conditions of both flow and weather. A higher inlet mass flow rate of nanofluids (Ag-water and Al3O2-water) was recommended both for better COP and handling nanoparticles deposition problem. In addition, due to thermal conductivity difference, the maximum COP of about 3 was achieved from PVT unit condenser with Ag-water as fluid medium. The optimum conditions of flow and weather were proposed for the operation of three considered PVT units condenser.

Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number (), Grashof number () and Richardson number () with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter () ratio of with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow (), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of on the hydrodynamic and thermal features. For constant friction factor and Nusselt number was observed to increase with increase in from 0.1 to 1.5 range. At fixed variation of heat flux leads to variation of or Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing On the other hand, the thermal entry length exhibited a decreasing trend with increasing Similarly, at constant Nusselt number increased with increasing for a range of 100–1000. It was evident that for a given and the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same and For a fixed the friction factor and Nusselt number decreased with increasing the Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor () with as well as and Nusselt number () with for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for with Graetz number () for developing and fully developed regimes in both assisting as well as opposing flows.

Macroscopic flow characterization at T-junctions

At T-junctions, a minor road meets a main road and merging vehicles from the minor road create traffic bottlenecks as significant interactions between vehicles occur. These interactions reduce road capacity resulting in congestion. The Lighthill-Whitham-Richards (LWR) model is widely employed to characterize traffic flow. However, this model only considers small changes in flow which can be inadequate for T-junctions. Thus, a new model is proposed which is based on driver response during transitions at these junctions. The proposed and LWR models are evaluated using the first order upwind scheme (FOUS). The Courant-Friedrich-Lewy (CFL) condition is employed to ensure model stability. Results are presented which show that the proposed model better characterizes traffic flow at T-junctions.

Analysis of nodalization uncertainty for nuclear system analysis code with Lax-Wendroff numerical scheme

In modeling the complex systems such as a nuclear power plant (NPP), the nodalization becomes more important to satisfy Courant number limitation and reduce the numerical diffusion due to the 1st order numerical scheme. Since the higher-order numerical scheme can reduce the numerical diffusion problem, the accuracy can be improved and the nodalization uncertainty can be reduced by improving the current numerical scheme. However, another sources for the user effect uncertainty originates from a nodalization process and this can be affected by the selected numerical scheme. Sufficient sensitivity analyses should be performed on the nodalization to ensure that the calculated results are free from these uncertainties. Therefore, in this study, the nodalization uncertainties of 1st order upwind scheme and Lax-Wendroff scheme are evaluated with the revised MARS-KS code. The analysis of the nodalization uncertainty is performed for the separate effect tests (SETs) such as subcooled boiling and reflood experiments. The nodalization uncertainty is analyzed with the error between the experimental data and the calculation results of 1st order upwind scheme or Lax-Wendroff scheme. Thus, when using Lax-Wendroff scheme, the more accurate results with decreased nodalization uncertainty can be obtained. For the reflood calculations, accurate and consistent prediction of maximum peak cladding temperature (PCT) and accurate prediction of quenching time were observed with Lax-Wendroff scheme. However, the quenching time may not be consistent depending on the user. In terms of the computational efficiency, the central processing unit (CPU) time is generally increased by 40% with Lax-Wendroff scheme.

Formation of Cavitation and Supercavitation in a Rectangular Shape Nozzle

Flow inside a rectangular shape nozzle is simulated in this study. Finite volume scheme is utilized as the main solver for the current study. Second order scheme is utilized to discretize pressure. Second order upwind scheme is utilized for solving momentum equation. Then the momentum equation is coupled with the continuity equation to obtain the pressure and velocity at each cell. Cavitation inception and super cavitation is also found and discussed in this study and the results were also verified with previous Winklhofer et al. experiments.

Finite-volume Eulerian solver for simulation of particle-laden flows for icing applications

Particle-laden flows can be encountered in a plethora of engineering applications, e.g., sediment transport, fluidized beds, vehicle soiling, and aircraft icing. The latter is caused by supercooled water droplets or ice crystals impacting and adhering to an aerodynamic surface during flight. Simulating such flows requires proper application of physical models through the use of particle flow solvers, which can rely on Lagrangian or Eulerian formulations for the solution of particle dynamics. Although Lagrangian formulations present certain advantages in terms of time resources and simplicity of implementation, Eulerian solvers can easily provide complete details of the particle flow field, such as volume fraction distribution. Several Eulerian solvers exist for the particle flow, although they rely on systems of coupled transport equations, which can be further simplified in order to reduce modeling and computational effort. Therefore, the current study presents an elaborated 2D finite-volume Eulerian solver for the resolution of the dynamics of particle-laden flows through the use of a system of decoupled transport equations. Additionally, we introduced a modification into the traditional decoupled formulation in order to allow the implementation of 2nd order upwind schemes for the convective terms. Two cases are used as test benchmarks to show that the solver effectively achieves mesh independence, convergence stability, and 2nd order accuracy. Also, the solver physical modeling capabilities are evaluated by comparing results against the ones obtained through the Lagrangian formulation, the Ansys FLUENT Eulerian solver and a set of experimental results. Therefore, the elaborated Eulerian solver can be used to facilitate the modeling of in-flight icing phenomena while still retaining the accuracy of traditional formulations.

TRITON: A Multi-GPU open source 2D hydrodynamic flood model

A new open source multi-GPU 2D flood model called TRITON is presented in this work. The model solves the 2D shallow water equations with source terms using a time-explicit first order upwind scheme based on an Augmented Roe's solver that incorporates a careful estimation of bed strengths and a local implicit formulation of friction terms. The scheme is demonstrated to be first order accurate, robust and able to solve for flows under various conditions. TRITON is implemented such that the model effectively utilizes heterogeneous architectures, from single to multiple CPUs and GPUs. Different test cases are shown to illustrate the capabilities and performance of the model, showing promising runtimes for large spatial and temporal scales when leveraging the computer power of GPUs. Under this hardware configuration, communication and input/output subroutines may impact the scalability. The code is developed under an open source license and can be freely downloaded in https://code.ornl.gov/hydro/triton.

Macroscopic Traffic Flow Characterization for Stimuli Based on Driver Reaction

The design and management of infrastructure is a significant challenge for traffic engineers and planners. Accurate traffic characterization is necessary for effective infrastructure utilization. Thus, models are required that can characterize a variety of conditions and can be employed for homogeneous, heterogeneous, equilibrium and non-equilibrium traffic. The Lighthill-Whitham-Richards (LWR) model is widely used because of its simplicity. This model characterizes traffic behavior with small changes over a long idealized road and so is inadequate for typical traffic conditions. The extended LWR model considers driver types based on velocity to characterize traffic behavior in non lane discipline traffic but it ignores the stimuli for changes in velocity. In this paper, an improved model is presented which is based on driver reaction to forward traffic stimuli. This reaction occurs over the forward distance headway during which traffic aligns to the current conditions. The performance of the proposed, LWR and extended LWR models is evaluated using the first order upwind scheme (FOUS). The numerical stability of this scheme is guaranteed by employing the Courant, Friedrich and Lewy (CFL) condition. Results are presented which show that the proposed model can characterize both small and large changes in traffic more realistically. Doi: 10.28991/cej-2021-03091632 Full Text: PDF

Wind Farm Fault Detection by Monitoring Wind Speed in the Wake Region

A novel concept of wind farm fault detection by monitoring the wind speed in the wake region is proposed in this study. A wind energy dissipation model was coupled with a computational fluid dynamics solver to simulate the fluid field of a wind turbine array, and the wind velocity and direction in the simulation were exported for identifying wind turbine faults. The 3D steady Navier–Stokes equations were solved by using the cell center finite volume method with a second order upwind scheme and a k−ε turbulence model. In addition, the wind energy dissipation model, derived from energy balance and Betz’s law, was added to the Navier–Stokes equations’ source term. The simulation results indicate that the wind speed distribution in the wake region contains significant information regarding multiple wind turbine faults. A feature selection algorithm specifically designed for the analysis of wind flow was proposed to reduce the number of features. This algorithm proved to have better performance than fuzzy entropy measures and recursive feature elimination methods under a limited number of features. As a result, faults in the wind turbine array could be detected and identified by machine learning algorithms.

Assessment of closure relations on the numerical predictions of vertical annular flows with the two-fluid model

In the present work, different closure relations in the one-dimensional Two-Fluid Model were investigated in order to assess the effect on the numerical simulation of vertical annular flows, including the formation and propagation of waves at the gas-liquid interface. Different interfacial friction formulations, momentum flux parameters and dynamic pressure terms were employed. The conservation equations were discretized and solved within the finite volume framework, with a first order time discretization, a second order TVD and first order Upwind schemes for the convective term. A rigorous mesh sensitivity analysis was performed, showing the advantages and shortcomings of each discretization scheme, as well as the impact of closure formulations and their importance for better physical representativeness and well-posedness. Flow and wave parameters were obtained with the different approaches for various test cases taken from the literature. A sensitivity analysis was performed with varying momentum flux parameter values, interfacial friction factors and dynamic pressure expressions. Liquid film thickness, pressure-drop and wave characteristics results were systematically compared to experimental data. Predictions for pressure gradient and mean liquid holdup with the best set of closures presented an average error of 9% and 22%. Comparison of the wave characteristics, given by the group speed and frequency with available measured values has shown that the model is capable to simulate the qualitative features of wave formation and propagation in vertical annular flow with a reasonable quantitative agreement, given the complexity of the physical phenomena involved. However, while it has been shown through the sensitivity analysis that the closure relations investigated here have an important effect on quantities of interest in annular flows, in particular that a momentum flux parameter value larger than unit seems beneficial, further investigations are suggested for a wider range of conditions, providing a robust physical support for the generalization of the closure model formulations.

Numerical Analysis of Turbulent Flow over a 2-D Prolate Spheroid

Recently external flow over body creates more interest of study because flow characteristics are dominated by complex phenomenon like separation and transition.in this paper turbulent flow over a 2-D prolate spheroid (6:1) is consider for analysis. Generation of surface grid around prolate spheroid by using grid generation code MESHGEN. Laminar and turbulent Flow past given geometry is simulated by Navier-stoke code RANS3D by second order upwind scheme for convective flux discretization by k-ε model for different Reynolds number, angles of attack .It is observed that the value of drag coefficient is lower than that of a cylinder due to its more streamlined contour. The variation of Cd was steeper in the laminar range than the turbulent range due to the effects of viscous forces being greater in laminar flow.

Quantifying hemodynamics within an aneurysm exposed to prolonged exercise levels

Background and objectiveNon-invasive treatment of unruptured Abdominal Aortic Aneurysm involves subjecting the patients to certain physiological levels of the heart. Flow topology (Repeak = 200–1200, frequency: f = 1.18–2.41 Hz) within an aneurysm geometry (2-D) under resting and exercise (mild and moderate) conditions are explored in the present study. Blood is assumed to be Newtonian in nature. Spatio-temporal evolution of the flow patterns and vorticity are established. Hemodynamic indicators (TAWSS and OSI), movement of vortex cores and Particle Residence Index (PRI) are quantified to select an optimum exercise level in attenuating the disease. MethodsThe finite volume method is employed for numerical solutions using ANSYS-FluentⓇ software. The SIMPLE scheme has been used for the pressure-velocity coupling. Least Square cell-based method is used for the spatial discretization of the gradients. Second order upwind scheme is considered for discretization of the pressure term. Third order upwind (QUICK) scheme is used to discretize the momentum equation. First order Implicit Scheme was used for the discretization of the temporal terms. Discrete Phase Material (DPM) technique is employed throughout, to visualize the signature of particle deposits within the aneurysm. ResultsVortex impingement induces a pressure peak within the aneurysm (moderate) while the peaks are anchored at the proximal and distal ends under resting and mild conditions. Along the averaged flow separation zone, exercise increases the maximum TAWSS from 1.21 N/m2 (mild) to 9.3 N/m2 (moderate). The distal site is exposed to oscillatory loading (OSI = 0.5) under mild activity whereas the loading becomes distributed almost over the entire wall, when subjected to moderate conditions. This in turn, reduces the time involved in 50 percent clearance of particles (PRI = 0.5) from 10.56 s (resting) to 3.98 s (mild) and 0.87 s (moderate), respectively. ConclusionsResting conditions manifests the aneurysmal wall to recirculating fluid for most of cycle time. Moderate exercise exhibits the least particle clearance time, but it exposes the aneurysmal wall and the distal end to high pressure, which otherwise has low intensity under mild activity. This in turn establishes that mild exercise for prolonged duration can be an optimum level for non-invasive aneurysmal treatment.

Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids

We address the problem of inverse design of linear hyperbolic transport equations in 2D heterogeneous media. We develop numerical algorithms based on gradient-adjoint methodologies on unstructured grids. While the flow equation is compulsorily solved by means of a second order upwind scheme so to guarantee sufficient accuracy, the necessity of using the same order of approximation when solving the sensitivity or adjoint equation is examined. Two test cases, including Doswell frontogenesis, are analysed. We show the convenience of using a low order method for the adjoint resolution, both in terms of accuracy and efficiency. An analytical explanation for this fact is also provided in the sense that, when employing higher order schemes for the adjoint problem, spurious high frequency numerical components slow down the convergence process.

A conservative viscous vorticity method for unsteady unidirectional and oscillatory flow past a circular cylinder

A conservative vorticity method for solving the 2-D incompressible unsteady viscous flow in the eulerian frame is proposed. The numerical method implements the vorticity-stream function formulation of the Navier–Stokes (N–S) equations, solved by the cell-centered Finite Volume Method (FVM). A convection limiter, coupling the first order upwind scheme and the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme, is introduced to maintain the accuracy and keep the monotonicity of vorticity interpolations. The vorticity induced stream functions are recovered by a closed-form expression, which also accurately predicts the far-field boundary conditions. The convective flux is evaluated by the difference of stream functions on the neighboring two nodes, which spontaneously eliminates the net mass flux out of a control cell. The conservative FVM and QUICK scheme and the definite evaluations of stream functions and convective flux guarantee the conservation of circulation and mass. The impulsively started flow past a circular cylinder at Reynolds numbers ranging from 100 to 9500 and the inline oscillatory flow around a circular cylinder at Reynolds numbers 100 and 200 are numerically simulated using this method. The current results under the inertial and non-inertial translational frame are well validated by comparisons with other numerical and experimental benchmark tests.

Comparison of varieties of numerical methods applied to lid-driven cavity flow: coupling algorithms, staggered grid vs. collocated grid, and FUDS vs. SUDS

The effectiveness of different methods, schemes, algorithms, and approaches is of substantial challenging problems in numerical modeling of transport phenomena. In the present paper, a lid-driven cavity problem is modeled via two basically different approaches of spatial discretization: collocated and staggered. The non-dimensionalized governing equations are semi-discretized by using a finite volume approach. Then, the full discretization is performed in each of collocated and staggered grids, separately. Upwind and central difference schemes are implemented in order to discretize the convective and diffusion terms of equations, respectively. After mesh independency study, the performances of collocated and staggered grids in comparison with the reference benchmark are presented. Next, the effectiveness of the first and the second order upwind schemes are presented, as well as different coupling algorithms of SIMPLE, SIMPLEC, and SIMPLER. Finally, an overall comparison of the methods is provided and acceptable agreements with benchmark are attained.