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Implementation of a smoothing pressure correction approach to the pressure-correction equation in order to maintain the use of simpleC algorithms on non-staggered grids

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PROGRESS IN COMPUTATIONAL FLUID DYNAMICS 2010年第1期10卷 40-50页

作者： Anany, M. N. Schnell, U. Scheffknecht, G. Univ Stuttgart Inst Proc Engn & Power Plant Technol D-70569 Stuttgart Germany

Date (1996) introduced a pressure-correction equation containing mass-conserving and smoothing pressure correction terms to solve the Navier-Stokes equations. The benefit of the smoothing terms is satisfying the stokes's relation which is often overlooked as well as overcoming the decoupling problem of the pressure-velocity fields, which renders it applicable to collocated (non-staggered) grids. His derivation relied on assumptions relevant to the simple algorithm (Caretto et al., 1972). Such assumptions are, unfortunately, not directly applicable to simpleC procedures (van Doormaal and Raithby, 1984). The main purpose of this paper is to extend the pressure-correction equation proposed by Date (1996) to simpleC algorithms.

关键词： colocated grid collocated grid non-staggered grid simple algorithm simpleC algorithm smoothing pressure corrections

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Analysis of quasi-steady combustion of Jatropha bio-diesel

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INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER 2008年第9期35卷 1079-1083页

作者： Rajesh, S. Raghavan, V. Shet, U. S. P. Sundararajan, T. Indian Inst Technol Madras Dept Mech Engn Chennai 600036 Tamil Nadu India

Quasi-steady gas-phase combustion of Jatropha bio-diesel in a mixed convective air environment is studied both experimentally and numerically. Porous sphere experiments have been conducted to measure the mass burning rates and observe the flame shapes of spherical particles fed with bio-diesel. A numerical model has been developed to simulate the experiments. The Jatropha bio-diesel has been considered as a single component fuel (C18H34O2). Transient governing equations in the gas-phase alone are solved through the finite volume approach employing non-orthogonal control volumes in a semi-collocated mesh. Thermo-physical properties are evaluated based on the local temperature and the species concentrations. A single step global reaction with five species (C18H34O2, O-2, N-2, CO2 and H2O) is employed to model the finite rate kinetics. Results have been obtained for a range of mixed convective flow conditions. Comparisons of the results with those of diesel combustion have been made in few cases. It is observed that the burning rate of bio-diesel is less by about 11% than those for diesel for the same air velocity and sphere size. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： quasi-steady combustion bio-diesel mixed convection simple algorithm

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NUMERICAL STUDY OF TURBULENT OFFSET JETS WITH ENTRAINMENT BOUNDARY

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1994年第1期8卷 182-184页

作者： YANG, YT YEH, YY National Cheng-Kung University Tainan Taiwan Republic of China

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An extension of the simple based discontinuous Galerkin solver to unsteady incompressible flows

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2015年第10期77卷 571-589页

作者： Klein, B. Kummer, F. Keil, M. Oberlack, M. Tech Univ Darmstadt Chair Fluid Dynam D-64287 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn D-64293 Darmstadt Germany Stanford Univ Ctr Turbulence Res Stanford CA 94305 USA Tech Univ Darmstadt Ctr Smart Interfaces D-64287 Darmstadt Germany

In this paper, we present a simple based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formulae (BDF) of varying order from 1 to 4. We show that the original equation for the pressure correction can be modified by using an equivalent operator stemming from the symmetric interior penalty (SIP) method leading to a reduced stencil *** assess the accuracy as well as the stability and the performance of the scheme, three different test cases are carried out: the Taylor vortex flow, the Orr-Sommerfeld stability problem for plane Poiseuille flow and the flow past a square cylinder. (1) Simulating the Taylor vortex flow, we verify the temporal accuracy for the different BDF schemes. Using the mixed-order formulation, a spatial convergence study yields convergence rates of k + 1 and k in the L-2-norm for velocity and pressure, respectively. For the equal-order formulation, we obtain approximately the same convergence rates, while the absolute error is smaller. (2) The stability of our method is examined by simulating the Orr-Sommerfeld stability problem. Using the mixed-order formulation and adjusting the penalty parameter of the symmetric interior penalty method for the discretization of the viscous part, we can demonstrate the long-term stability of the algorithm. Using pressure stabilization the equal-order formulation is stable without changing the penalty parameter. (3) Finally, the results for the flow past a square cylinder show excellent agreement with numerical reference solutions as well as experiments. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： finite element discontinuous Galerkin Navier-Stokes incompressible flow segregated solution algorithms simple algorithm

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Natural convection in a trapezoidal enclosure with offset baffles

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2001年第2期15卷 212-218页

作者： Moukalled, F Acharya, S Amer Univ Beirut Dept Mech Engn Beirut Lebanon Louisiana State Univ Dept Mech Engn Baton Rouge LA 70803 USA

A numerical investigation has been made of natural convection heat transfer in a trapezoidal enclosure (representing attic spaces) with offset baffles. Two thermal boundary conditions representing summerlike conditions (upper surface heated) and winterlike conditions (upper surface cooled) and two baffle heights are studied. For each boundary condition and baffle height, two baffle positions are considered. In position I, the upper baffle is offset toward the heated vertical wall and the lower baffle is offset toward the symmetry plane of the enclosure, whereas in position II, the upper baffle is offset toward the symmetry plane and the lower baffle is offset toward the heated wall. Rayleigh number values range from 10(3) to 5 x 10(7) for summerlike conditions and from 10(3) to 10(6) for winterlike conditions. Predictions reveal a decrease in heat transfer in the presence of baffles. In winterlike conditions, convection starts to dominate at a Rayleigh number much lower than that in summerlike conditions. The maximum reduction in heat transfer is achieved with long baffles placed in position II for summerlike conditions and in position I for winterlike conditions. Average Nusselt number correlation for both boundary conditions are presented.

关键词： Natural Convection Thermal Boundary Condition Isotherms Conduction Vortices Thermal Conductivity simple algorithm Numerical Modeling Jet Stream Conservation Equations

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A free element scheme for simulating two- and three-dimensional incompressible fluid flow

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2021年第4期93卷 1163-1182页

作者： Liu, Hua-Yu Gao, Xiao-Wei Xu, Bing-Bing Dalian Univ Technol Sch Aeronaut & Astronaut Dalian Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian Peoples R China

In this work, Free Element method (FECM) is extended to solve incompressible Navier-Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoints are interpolated by improved Momentum Interpolation Method to avoid oscillation caused by decoupling of velocity and pressure. At last, the pressure correction equation is solved to make sure the results satisfying continuity equation. The interpolation of midpoint's velocity is proved to be independent of the under-relaxation factor and time step size. The deferred correction is employed for utilization of higher-order discretization of convective terms. Taylor-Green vortex, flow over a cylinder, lid-driven flow, cooling tunnel, and flow over airfoil are simulated. The results computed by the proposed method are compared with exact solutions and benchmark solutions, which indicates that the new method has the second order accuracy in space. What is more, the proposed method works well on random node distributions as well, which means that the method is much robust.

关键词： free element method incompressible flow momentum interpolation Navier‐ Stokes equations simple algorithm

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Numerical study for the assessment of pollutant dispersion from a thermal power plant under the different temperature regimes

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INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCE AND TECHNOLOGY 2019年第10期16卷 6089-6112页

作者： Issakhov, A. Mashenkova, A. Al Farabi Kazakh Natl Univ Alma Ata Kazakhstan Kazakh British Tech Univ Alma Ata Kazakhstan

In this paper, numerical simulation of motion and dispersion of pollutant emissions into the atmosphere under real atmospheric conditions were considered. To solve this problem, a system of Reynolds-averaged Navier-Stokes equations was used, and the standard k-epsilon and SST k-omega turbulence models were used to close this system of equations. Moreover, the test problem was solved numerically to verify the mathematical model and numerical algorithm. The obtained numerical results were compared with the experimental data and modeling results of well-known authors. A proven mathematical model and numerical algorithm was used to describe the process of pollutant emissions from Ekibastuz SDPP (Ekibastuz State District power plant) chimneys and the spread of CO2 in the air flow field under real atmospheric conditions. For this problem, four different speed regimes (the first-0.5 m/s and 1 m/s, the second-1 m/s and 1.5 m/s, the third-2 m/s and 4 m/s, and the fourth-4 m/s and 5 m/s), as well as three different temperature regimes (constant temperature, decrease temperature, and temperature inversion) were considered.

关键词： Reynolds-averaged Navier-Stokes (RANS) Jet in crossflow Pollutant dispersion simple algorithm Temperature inversion

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On the stabilization of finite volume methods with co-located variables for incompressible flow

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 297卷 84-89页

作者： Klaij, C. M. Maritime Res Inst Netherlands NL-6700 AA Wageningen Netherlands

Finite volume methods with co-located variables for incompressible flow suffer from spurious pressure oscillations unless a stabilization method is applied. Variations of the pressure-weighed interpolation (PWI) method are typically used for this purpose. But the PWI method does not only prevent spurious oscillations. Counter-intuitively, it also simplifies the approximation of the Schur complement (pressure matrix) which appears in iterative solution methods such as simple. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Finite volume method Incompressible flow Co-located variables Velocity-pressure decoupling Pressure-weighted interpolation simple algorithm

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Modelling of Flow-Shear Coupling Process in Rough Rock Fractures Using Three-Dimensional Finite Volume Approach

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ROCK MECHANICS AND ROCK ENGINEERING 2019年第11期52卷 4693-4713页

作者： Karimzade, Ebrahim Seifabad, Masoud Cheraghi Sharifzadeh, Mostafa Baghbanan, Alireza Isfahan Univ Technol Dept Min Engn Esfahan Iran Curtin Univ Western Australian Sch Mines Dept Min & Met Engn Bentley WA Australia

A computational code has been developed based on finite-volume method (FVM) to investigate fluid flow-through roughwalled rock fractures during shear processes, considering evolutions of aperture and contact area with shear displacement. In the code, the full 3-D Navier-Stokes equation is solved in a cell-centered collocated variable arrangement and the pressure-velocity coupling is performed using the simple algorithm. A series of coupled shear-flow tests under constant normal stress of 3 MPa with different shear displacements of 1-10 mm were conducted and their results were compared with numerical simulations results. The comparison shows good agreement between the simulated and measured results. Aperture distribution during shear was evaluated by superimposing the upper and lower fracture surfaces according to the initial aperture and dilation at different shear displacements. The results show that contact area evolution dominates the variations of flow rate as well as flow pattern in a rough fracture. In addition, there is a linear relationship between aperture coefficient of variation and contact area ratio during shear. The simulation results also demonstrate the deviation of velocity profiles from the ideal parabolic form in some regions due to the formation of eddy flows. This behavior may have been caused by the inertial effects, which can be characterized by the Navier-Stokes equation, while some simplified equations such as Reynolds equation or Stokes equation cannot capture these effects.

关键词： Rough-walled rock fracture 3-D Navier-Stokes Contact area evolution Finite-volume method simple algorithm

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CALCULATION OF TURBULENCE-DRIVEN SECONDARY MOTION IN DUCTS WITH ARBITRARY CROSS-SECTION

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AIAA JOURNAL 1991年第4期29卷 531-537页

作者： DEMUREN, AO NASA LEWIS RES CTR INST COMPUTAT MECH PROP CLEVELAND OH 44135 USA

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered in the present study. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. The importance of the secondary Reynolds shear stress is stressed, but there are no reliable experimental data for this component. Model predictions are compared to experimental data for developed flow in a triangular duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with measured data.

关键词： Turbulence Stress Distribution Logarithmic Law of the Wall Continuity Equation Velocity Profiles Kinetic Energy Turbulence Models Turbulent Flow simple algorithm Aspect Ratio

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