Generalized Simplified Marker And Cell Research Articles

An application of GSMAC–FEM to coupled natural and Marangoni convection in a square cavity

This paper presents an efficient numerical scheme for the analysis of coupled natural and Marangoni convection encouraged by the thermal radiation. The novel feature of the proposed algorithm is the introduction of the jump quantity on the free surface into the boundary integration term in the Navier–Stokes equation discretized by the finite element method (FEM). In addition, the generalized simplified marker and cell (GSMAC) method is applied to the solution of the velocity field, which realizes high-speed computation. In order to verify the validity of the present scheme, two-dimensional (2D) and three-dimensional (3D) numerical simulation of coupled natural and Marangoni convection in a square cavity is performed for a wide range of Marangoni number and Grashof number: Numerical results obtained here are in good agreement with the experimental data, and the dominance of Marangoni convection is clearly shown with the increase of Marangoni number.

Numerical analysis of thermal melt flow and melt/solid interface shapes in the floating zone method

Numerical simulation of the thermal melt flow coupled with moving melt/solid interfaces in the floating zone (FZ) method under low gravity is carried out. The novel feature of the proposed algorithm is the application of the arbitrary Lagrangian–Eulerian (ALE) method to the moving melt/solid interface problem. The governing equations are discretized by the finite element method (FEM), and the velocity field is solved by the generalized simplified marker and cell (GSMAC) method. The developed scheme is employed to investigate the two-dimensional (2D) melt flow and melt/solid interface shapes in various conditions of gravity and surface tension. Through computation, it is revealed that the melt/solid interface shape is greatly affected by the flow configuration and the intensity of convection. Moreover, coupled natural and Marangoni convection reduces the stability of the melt zone; for the conditions in the present study, the flow configuration and the melt/solid interface shape are suddenly changed as soon as natural convection is merged into Marangoni convection as a consequence of increased gravity. The usefulness of the transverse magnetic field in control of the melt flow is also clarified through the comparison with the vertical magnetic field.

Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement

AbstractA novel numerical scheme is developed by coupling the level set method with the adaptive mesh refinement in order to analyse moving interfaces economically and accurately. The finite element method (FEM) is used to discretize the governing equations with the generalized simplified marker and cell (GSMAC) scheme, and the cubic interpolated pseudo‐particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh refinement is implemented in the quadrangular grid systems and easily embedded in the FEM‐based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two‐dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its effectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni effect is first simulated efficiently with the present scheme. Copyright © 2004 John Wiley & Sons, Ltd.

Large Eddy Simulation of a Turbulent Channel Flow Using Dynamic SGS Model with GSMAC-FEM

The purpose of our study is to analyze the engineeringly turbulent flows. In these case, LES (Large Eddy Simulation) is expected to be the most effective method. Since three dimensional unsteady calculation is carried out in LES, it is possible to understand the flow visually using computer graphic system and to offer useful information. In order to achieve the purpose, it is necessary to analyze the benchmark problem and to show the effectiveness in the first step. In this paper, a turbulent channel flow at Reτ = 360 based on the friction velocity uτ and channel width δ is analyzed using the Dynamic Smagorinsky model with GSMAC (Generalized Simplified Marker and Cell) FEM. In order to confirm its effectiveness, numerical results are compared with the DNS data and other results and the present scheme is verified.

Numerical study of flows with multiple free surfaces

AbstractThis paper demonstrates that a numerical method based on the generalized simplified marker and cell (GENSMAC) flow solver and Youngs' volume of fluid (Y‐VOF) surface‐tracking technique is an effective tool for studying the basic mechanics of hydraulic engineering problems with multiple free surfaces and non‐hydrostatic pressure distributions. Two‐dimensional flow equations in a vertical plane are solved numerically for this purpose. The numerical results are compared with experimental data and earlier numerical results based on a higher‐order depth‐averaged flow model available in the literature. Two classical problems, (i) flow in a free overfall and (ii) flow past a floor slot, are considered. The numerical results correspond very well with the experimental data for both sub‐critical and supercritical flows. Copyright © 2001 John Wiley & Sons, Ltd.

Unified Solution Algorithm for Solids and Fluids

In this work, we propose a new unified-solution algorithm for solids and fluids using generalized simplified marker and cell (GSMAC)-finite element method (FEM). We use the Lagrangian description for displacement vector fields in solids, and, the Eulerian description for velocity vector fields in fluids. We carried out the analysis for static beam bending problems and dynamic viscoelastic response problems in order to the verify the validity of the present scheme for the solid phase. Additionally the analysis of self-excited oscillations of a cylinder in uniform flow is performed as a coupled vibration problem between the fluid and solid.

Analysis of Non-Newtonian Fluids by GSMAC-FEM. Flow of Carreau Fluids through an Axisymmetric Abrupt Contraction.

In a previous paper, we proposed a simple, low-storage finite element scheme for three-dimensional flow analysis of non-Newtonian fluids. The scheme is based on the GSMAC (generalized simplified marker and cell) finite element method, and employs rational Runge-Kutta time integration in order to maintain stability for high viscosity flow. In the present work, the flow of Carreau fluids through an axisymmetric abrupt contraction is calculated to confirm the applicability of the present scheme at low shear rates. The numerical results agree with numerical solutions calculated by Kim et al., and by means of comparing the results for two contraction ratios (1 : 4, 1 : 2), we investigate how the contraction ratio affects the velocity profiles at the plane of contraction and the pressure drop distance.

Numerical Analysis of Natural Convection in Thermoelectrically Conducting Fluids in a Cubic Cavity under a Constant Magnetic Field. 1st Report. Effect of Perpendicular Magnetic Field, Comparison of Visualized Experimental Results.

When electromagnetic fields are applied to thermoelectrically conducting fluids such as melted metals, the velocity, electromagnetic and temperature distributions are interrelated. Therefore the behavior of thermoelectrically conducting fluids is complicated under electromagnetic fields. In this work, we propose coupling GSMAC (generalized simplified marker and cell) finite element method with the φ-method, and discuss the natural convection of a thermoelectrically conducting fluid in a cubic cavity under a constant magnetic field. In the case of mercury (Prandtl number Pr=0.025, Grashof number Gr=3.75×107) under a magnetic field, the temperature distributions obtained using the present numerical method agree qualitatively with the visualized experimental results, obtained using a thermosensitive liquid crystal sheet.

Flow Induced Vibrations in Engineering Systems and the Control of Flow induced Vibrations. Prediction of the Acoustic Instabilities of Tube Arrays in Cross Flow using Numerical Analysis.

The acoustic exciting forces in a duct where a bundle of tubes are in staggered arrangement at a pitch-to-diameter ratio of 2.0 were analyzed using a finite-volume technique which the authors developed on the basis of the GSMAC (Generalized Simplified Marker and Cell) method. Forced oscillating flows with a constant frequency which are perpendicular to a main flow were employed for the analysis of the acoustic vibration field. The fluctuating lift forces on individual tubes in the flow field where the main flow and oscillating flows exist were calculated two-dimensionally. The calculated lift amplitude and the calculated phase difference between the fluctuating lift and the acceleration of forced oscillation, which affects the stability of the acoustic vibration were in good agreement with the values measured in experiment. The finite-volume technique can now be applied to the analysis of acoustic vibrations in the sound field of a duct installed with a bundle of tubes arranged differently.

Numerical Analysis of Natural Convection of Thermoelectrically Conducting Fluids in a Square Cavity under a Uniform Magnetic Field. Estimation of Induced Heating Term.

The applications of MHD (magnetohydrodynamics) devices have been rapidly developed in recent years. Thermoelectrically conducting fluid has been increasingly used in the manufacturing process of semiconducting materials such as silicon crystal. In the present paper, we propose a new GSMAC (generalized simplified marker and cell)finite-element method coupled with the B method. The present scheme efficiently satisfies both conservation laws of mass and magnetic flux. In order to verify the present scheme, we discuss the natural convection of thermoelectrically conducting fluids in a square cavity under a uniform magnetic field. The numerical results obtained here agreed well with previous experimental and numerical results. Moreover, we estimate the effect of the induced heating term on a temperature field.

AN APPLICATION OF GSMAC-FEM TO ELECTRICALLY CONDUCTING FLUID FLOWS DRIVEN BY LORENTZ FORCE

ABSTRACT A new finite element method for incompressible, electrically conducting fluid flow is presented. This method satisfies the conservation laws of mass, magnetic flux and electric current. The main algorithm of the GSMAC (generalized simplified marker and cell) method is employed in order to satisfy the solenoidal conditions of both magnetic and electric current fields. The flow between two parallel plates, driven by electromagnetic forces are calculated to verify this new method. Numerical results obtained here agree with other numerical results or exact solutions. M-shape axial velocity profiles are clearly simulated by GSMAC—FEM near the electrode between two parallel plates as shown in Figure 1.

Numerical Analysis of Natural Convection of Thermo-Electrically Conducting Fluids in a Square Cavity under a Constant Magnetic Field. 1st Report. Estimation of Induced Heating Term.

The applications of MHD (magnetohydrodynamics) devices have been rapidly developed in recent years. Thermo-electrically conducting fluid has been increasingly used in the manufacturing process of semiconducting material such as silicon crystal. In the present paper, we propose a new GSMAC (generalized simplified marker and cell) finite element method coupling with the B method. The present scheme efficiently satisfies both conservation laws of mass and magnetic flux. In order to verify the present scheme, we discuss the natural convection of thermo-electrically conducting fluids in a square cavity under a constant magnetic field. The numerical results obtained here agreed well with the past experimental and numerical results. Moreover, we estimate the effect of the induced heating term on a temperature field.

Numerical Analysis of Nonlinear Water Waves Using Arbitrary Lagrangian-Eulerian Finite Element Method.

Since free surface flows are seen in nature phenomena and artificial systems, the analysis for these flows has been more important in mechanical engineering. However, theoretical analyses are almost impossible because the boundary conditions are nonlinear equations in analyzing the free surface flows. Thus, numerical analyses are needed. Finite element method (FEM) which can be used for unstructured grid can easily treat boundary conditions. Thus, FEM is used in many technological fields. In this thesis, free surface flow problems were analyzed using the finite element method. In solving these problems, an arbitrary Lagrangian-Eulerian (ALE) kinematical description of the fluid domain was adopted, in which the nodal point can be displaced independently of the fluid motion. The ALE method was introduced into the Generalized Simplified Marker and Cell (GSMAC) method. Damping out the alternating errors was examined in this scheme.

GSMAC有限要素法による熱対流のシミュレーション

GSMAC (Generalized simplified marker and cell) method which is the fast FEM scheme for incompressible flow is applied to two-dimensional heat convection. Natural convection within horizontal annulus and natural convection within a semicircle heated below are numerically investigated. Numerical results of the natural convection within the horizontal annulus are in good agreement with experimental results at Prandtl number Pr=0.71 and Rayleigh number Ra=4.7×104. In the case of the natural convection within the semicircle heated below, interesting unsteady motions of hot thermal plumes are simulated at Pr=9.0 and Ra=1.0×105. Numerical results show that the GSMAC method is effective in order to predict the heat convection problems.