scholarly journals An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations

2019 ◽  
Vol 136 ◽  
pp. 139-151 ◽  
Author(s):  
Zeting Liu ◽  
Fawang Liu ◽  
Fanhai Zeng
Keyword(s):  
Spectral Method ◽  
Wave Equations ◽  
Two Dimensional ◽  
Diffusion Wave ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
And Diffusion

ADI Galerkin FEMs for the 2D nonlinear time-space fractional diffusion-wave equation

2017 ◽  
Vol 08 (03) ◽  
pp. 1750025 ◽  
Author(s):  
Meng Li ◽  
Chengming Huang
Keyword(s):  
Wave Equations ◽  
Numerical Technique ◽  
Fractional Diffusion ◽  
Spatial Direction ◽  
Diffusion Wave ◽  
Alternating Direction Implicit ◽  
Galerkin Finite Element ◽  
Time Space ◽  
Alternating Direction ◽  
Temporal Derivative

In this paper, we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative. Galerkin finite element scheme is used for the discretization in the spatial direction, and the temporal component is discretized by a new alternating direction implicit (ADI) method. Next, we strictly prove that the numerical method is stable and convergent. Finally, to confirm our theoretical analysis, some numerical examples in 2D space are presented.

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.

Numerical Solutions of Nonsteady Two-Dimensional Transonic Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 341-347 ◽  
Author(s):  
M. Couston ◽  
J. J. Angelini
Keyword(s):  
Numerical Solutions ◽  
Low Frequency ◽  
Two Dimensional ◽  
Lattice Method ◽  
Alternating Direction Implicit ◽  
Flow Problems ◽  
Present Procedure ◽  
Alternating Direction ◽  
Trailing Edge Flaps ◽  
Doublet Lattice Method

An alternating-direction implicit algorithm is applied to solve an improved formulation of the low-frequency, small-disturbance, two-dimensional potential equation. Linear solutions are presented for oscillating trailing edge flaps, plunging and pitching flat-plate airfoils, and compared with results obtained by a doublet-lattice-method. Nonlinear calculations for both steady and unsteady flow problems are then compared with results obtained by using the complete Euler equations. The present procedure allows one to solve complex aerodynamic problems, including flows with shock waves.

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