Numerical Study of Transient and Steady Induced Symmetric Flows in Rectangular Cavities

1977 ◽  
Vol 99 (3) ◽  
pp. 526-530 ◽  
Author(s):  
B. S. Jagadish
Keyword(s):  
Steady State ◽  
Stream Function ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Aspect Ratios ◽  
Alternating Direction ◽  
Vorticity Transport ◽  
Steady State Solutions

Symmetric flows induced in rectangular cavities by a pair of moving walls are studied numerically. Solutions are obtained by solving the coupled transient vorticity transport and stream function relations using the alternating direction implicit method. Steady state solutions are obtained as limiting cases of the transients. The study covers Reynolds numbers of 1 100 and 1000 for cavities having aspect ratios of 0.5 and 1.0.

scholarly journals Pedestrian Walking Behavior Revealed through a Random Walk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hui Xiong ◽  
Liya Yao ◽  
Huachun Tan ◽  
Wuhong Wang
Keyword(s):  
Numerical Experiments ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Pedestrian Flow ◽  
Alternating Direction Implicit Method ◽  
Walking Behavior ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Continuous Time Random Walks ◽  
High Order Compact Scheme

This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

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.

scholarly journals Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Markus Gasteiger ◽  
Lukas Einkemmer ◽  
Alexander Ostermann ◽  
David Tskhakaya
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Vlasov Equation ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Time Integration ◽  
Computational Effort ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Wide Range

The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov-based methods such as the generalized minimal residual method (GMRES) or relaxation schemes) is computationally expensive. In the former case the slowest time scale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an alternating direction implicit type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speed-up of close to two orders of magnitude (even for intermediate grid sizes) with respect to the unpreconditioned case. In addition, we discuss the characteristics of these numerical methods and show the results for a number of numerical simulations.

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