Implicit Multigrid Computations of Buoyant Drops Through Sinusoidal Constrictions

2004 ◽  
Vol 71 (6) ◽  
pp. 857-865 ◽  
Author(s):  
Metin Muradoglu ◽  
Seckin Gokaltun
Keyword(s):  
Multigrid Method ◽  
Front Tracking ◽  
Computational Domain ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Front Tracking Method ◽  
Time Stepping ◽  
Alternating Direction ◽  
Dual Time Stepping ◽  
Constricted Channel

Two-dimensional computations of dispersed multiphase flows involving complex geometries are presented. The numerical algorithm is based on the front-tracking method in which one set of governing equations is written for the whole computational domain and different phases are treated as a single fluid with variable material properties. The front-tracking methodology is combined with a newly developed finite volume solver based on dual time-stepping, diagonalized alternating direction implicit multigrid method. The method is first validated for a freely rising drop in a straight channel, and it is then used to compute a freely rising drop in various constricted channels. Interaction of two buoyancy-driven drops in a continuously constricted channel is also presented.

Comparative Numerical Simulation of Natural Convection in a Porous Horizontal Cylindrical Annulus

2014 ◽  
Vol 670-671 ◽  
pp. 613-616 ◽  
Author(s):  
Jabrane Belabid ◽  
Abdelkhalek Cheddadi
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Published Data ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Concentric Cylinders ◽  
Good Agreement

This work presents a numerical study of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method and the Samarskii-Andreev scheme. A comparison between the two methods is conducted. In both cases, the results obtained for the heat transfer rate given by the Nusselt number are in a good agreement with the available published data.

Integration of Navier-Stokes equations using dual time stepping and a multigrid method

AIAA Journal ◽  
1995 ◽  
Vol 33 (6) ◽  
pp. 985-990 ◽  
Author(s):  
Andrea Arnone ◽  
Meng-Sing Liou ◽  
Louis A. Povinelli
Keyword(s):  
Multigrid Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Dual Time Stepping

scholarly journals Preservation of Fine Structures in PDE-Based Image Denoising

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Hakran Kim ◽  
Velinda R. Calvert ◽  
Seongjai Kim
Keyword(s):  
Numerical Methods ◽  
Image Denoising ◽  
Numerical Technique ◽  
Significant Loss ◽  
Implicit Time ◽  
Alternating Direction Implicit ◽  
Time Stepping ◽  
Alternating Direction ◽  
Fine Structures ◽  
Efficiency And Reliability

Image denoising processes often lead to significant loss of fine structures such as edges and textures. This paper studies various innovative mathematical and numerical methods applicable for conventional PDE-based denoising models. The method of diffusion modulation is considered to effectively minimize regions of undesired excessive dissipation. Then we introduce a novel numerical technique for residual-driven constraint parameterization, in order for the resulting algorithm to produce clear images whose corresponding residual is as free of image textures as possible. A linearized Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to simulate the resulting model efficiently. Various examples are presented to show efficiency and reliability of the suggested methods in image denoising.

scholarly journals Effect of Perpendicular Magnetic Field on Free Convection in a Rectangular Cavity

2015 ◽  
Vol 20 (2) ◽  
pp. 49 ◽  
Author(s):  
Anand Kumar ◽  
Ashok K. Singh ◽  
Pallath Chandran ◽  
Nirmal C. Sacheti
Keyword(s):  
Magnetic Field ◽  
Stream Function ◽  
Governing Equations ◽  
Free Convective Flow ◽  
Alternating Direction Implicit ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Alternating Direction ◽  
Vertical Walls ◽  
The Magnetic Field

The steady free convective flow of a viscous incompressible and electrically conducting fluid in a two-dimensional cavity in the presence of a magnetic field applied normal to the plane of the cavity is investigated. The side vertical walls of the cavity are heated differentially while the horizontal walls are assumed to be insulated. The governing equations are re-formulated in terms of vorticity and stream function. The resulting boundary value problem is solved numerically using an alternating direction implicit (ADI) method. A number of plots illustrating the influence of Hartmann number and Rayleigh number on the streamlines and isotherms as well as the velocity and temperature profiles are shown. Furthermore, results for the average Nusselt number and the maximum absolute stream function have been obtained, and these are compared with the corresponding results in the literature when the magnetic field is applied along the cavity in the horizontal direction.  

scholarly journals Numerical methods for time-fractional convection-diffusion problems with high-order accuracy

2021 ◽  
Vol 19 (1) ◽  
pp. 782-802
Author(s):  
Gang Dong ◽  
Zhichang Guo ◽  
Wenjuan Yao
Keyword(s):  
High Order Accuracy ◽  
Order Accuracy ◽  
Alternating Direction Implicit ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Time Stepping ◽  
Alternating Direction ◽  
Special Cases ◽  
Compact Adi Scheme ◽  
Convergence Of The Scheme

Abstract In this paper, we consider the numerical method for solving the two-dimensional time-fractional convection-diffusion equation with a fractional derivative of order α \alpha ( 1 < α < 2 1\lt \alpha \lt 2 ). By combining the compact difference approach for spatial discretization and the alternating direction implicit (ADI) method in the time stepping, a compact ADI scheme is proposed. The unconditional stability and H 1 {H}^{1} norm convergence of the scheme are proved rigorously. The convergence order is O ( τ 3 − α + h 1 4 + h 2 4 ) O\left({\tau }^{3-\alpha }+{h}_{1}^{4}+{h}_{2}^{4}) , where τ \tau is the temporal grid size and h 1 {h}_{1} , h 2 {h}_{2} are spatial grid sizes in the x x and y y directions, respectively. It is proved that the method can even attain ( 1 + α ) \left(1+\alpha ) order accuracy in temporal for some special cases. Numerical results are presented to demonstrate the effectiveness of theoretical analysis.

Numerical Investigation of Magneto-Natural Heat Transfer in Nanofluid Filled Inclined Enclosure

2020 ◽  
Vol 9 (2) ◽  
pp. 98-105
Author(s):  
L. Eljamali ◽  
R. Sehaqui
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Inclined Enclosure ◽  
Vertical Walls

This paper examines the natural convection in an inclined enclosure that is filled with a water-copper nanofluid and influenced by a magnetic field applied normal to the plane of the cavity. The horizontal walls are assumed to be insulated while the side vertical walls of the cavity are heated differentially. The governing equations are re-formulated in functions of stream function and vorticity. The resulting boundary value problem is solved numerically using an ADI method (alternating direction implicit). A variety of plots showing the velocity and temperature profiles and the influence of Hartmann number as well as Rayleigh number on the streamlines and isotherms are shown.

scholarly journals Theoretical Modeling of the Vapor Cavitation in Dynamically Loaded Journal Bearings

1986 ◽  
Vol 108 (4) ◽  
pp. 628-637 ◽  
Author(s):  
D. E. Brewe
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Control Volume ◽  
Circular Path ◽  
High Speed Photography ◽  
Computational Domain ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Dynamically Loaded ◽  
Volume Method

A theoretical investigation is made of the evolution of a vapor bubble for a submerged journal bearing under dynamically loaded conditions. The solution to the Reynolds equation is determined numerically using a control volume method (Elrod algorithm). This method conserves mass throughout the computational domain including the liquid-vapor interface which may or may not be in motion relative to the minimum film line. An ADI (Alternating Direction Implicit) method is used to effect the time march. Excellent agreement was found with the experimental work of Jakobsson and Floberg for stationary cavitation. Predictions of bubble life for nonstationary cavitation compare reasonably well with that measured by Jacobson and Hamrock using high-speed photography. A comparison study was performed to determine some of the consequences of applying a nonconservative theory to a dynamic problem. A complete dynamic cycle of a journal whirling in a circular path was chosen for the basis of comparison. Significant differences were observed in the load components near the end of the cycle. In each case, onset of cavitation was observed followed by bubble growth and subsequent collapse. More complete details of this phenomena are illustrated with the use of perspective graphic plots depicting the associated pressure distribution and region of cavitation with position and motion of the journal within the housing.

Impact of Wall Waviness on the Convection Patterns Inside a Horizontal Porous Annulus

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Jabrane Belabid
Keyword(s):  
Boussinesq Approximation ◽  
Darcy Law ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Convective Instabilities ◽  
Alternating Direction ◽  
Alternating Direction Implicit Scheme ◽  
Convection Patterns ◽  
The Mathematical Model ◽  
Hydrodynamics Equations

Abstract A numerical simulation of natural convection in a horizontal porous annulus with an internal wavy surface has been carried out. Governing equations include the heat equation and the hydrodynamics equations under Darcy law and Boussinesq approximation. The mathematical model formulated with the temperature-stream function is solved numerically using the finite difference method with the alternating direction implicit scheme. Results show that the heat transfer and the convective instability depend strongly on the waviness of the inner cylinder. Last, streamlines and isotherms are presented for different waviness parameters of the internal wall for better understanding of the influence of amplitude and number of undulations on the thermo-convective instabilities.

scholarly journals A One-Step Leapfrog ADI Procedure with Improved Absorption for Fine Geometric Details

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1135
Author(s):  
Peiyu Wu ◽  
Han Yu ◽  
Yongjun Xie ◽  
Haolin Jiang ◽  
Toshiaki Natsuki
Keyword(s):  
Stability Condition ◽  
Computational Domain ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
Numerical Examples ◽  
Alternating Direction ◽  
One Step ◽  
Overall Performance ◽  
The Stability ◽  
Stable Scheme

Based on the alternating direction implicit (ADI) procedure, leapfrog formulation, and a higher order PML scheme, we propose an unconditionally stable perfectly matched layer (PML) algorithm with improved absorption to treat open regions in a finite computational domain with improved overall performance. The proposed algorithm performed well compared to other algorithms during simulations. We further demonstrated the proposed scheme’s effectiveness using numerical examples. We found that the proposed scheme had enhanced effectiveness and improved the absorption during the whole simulation. Furthermore, it was able to break the stability condition, proving that it is an unconditionally stable scheme.

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