A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers

2015 ◽  
pp. 245-255
Author(s):  
Stephen Russell ◽  
Niall Madden
Keyword(s):  
Diffusion Problem ◽  
Sparse Grid ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Grid Technique

scholarly journals Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1878
Author(s):  
Eyaya Fekadie Anley ◽  
Zhoushun Zheng
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Diffusion Problem ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Finite Domain ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Nicolson Scheme ◽  
Crank Nicolson

In this paper, we have considered a numerical difference approximation for solving two-dimensional Riesz space fractional convection-diffusion problem with source term over a finite domain. The convection and diffusion equation can depend on both spatial and temporal variables. Crank-Nicolson scheme for time combined with weighted and shifted Grünwald-Letnikov difference operator for space are implemented to get second order convergence both in space and time. Unconditional stability and convergence order analysis of the scheme are explained theoretically and experimentally. The numerical tests are indicated that the Crank-Nicolson scheme with weighted shifted Grünwald-Letnikov approximations are effective numerical methods for two dimensional two-sided space fractional convection-diffusion equation.

ON ONE EFFECTIVE DIFFERENCE SCHEME FOR THE CONVECTION‐DIFFUSION PROBLEM

2001 ◽  
Vol 6 (2) ◽  
pp. 231-240
Author(s):  
G. Gromyko
Keyword(s):  
Difference Scheme ◽  
Iterative Algorithm ◽  
Diffusion Problem ◽  
Point Of View ◽  
Numerical Calculations ◽  
Test Problems ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
The Given ◽  
And Diffusion

The given paper is devoted to build‐up of the special economic difference schemes for non‐stationary one and two‐dimensional problems of a convection ‐ diffusion permitting to take into account convective and diffusion terms from the uniform point of view. On the basis of a multicomponent schemes build‐up procedure, bound up with region decomposition of the cells of mesh, the economic multicomponent iterative algorithm is constructed. A series of numerical calculations on some test problems solution including Burgers problem is reduced, and the comparison with known, most spread schemes is proceeded.

scholarly journals The combination technique for a two-dimensional convection-diffusion problem with exponential layers

2009 ◽  
Vol 54 (3) ◽  
pp. 203-223 ◽  
Author(s):  
Sebastian Franz ◽  
Fang Liu ◽  
Hans-Görg Roos ◽  
Martin Stynes ◽  
Aihui Zhou
Keyword(s):  
Diffusion Problem ◽  
Two Dimensional ◽  
Combination Technique ◽  
Convection Diffusion

scholarly journals The difference scheme for the two-dimensional convection-diffusion problem for large peclet numbers

2018 ◽  
Vol 226 ◽  
pp. 04030 ◽  
Author(s):  
Alexander I. Sukhinov ◽  
Alexander E. Chistyakov ◽  
Yulia V. Belova
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Difference

The purpose of this work is the development of a difference scheme for the solution of convection-diffusion problem at high Peclet numbers (Pe>2). In accordance with this purpose the following problems were solved: difference scheme for convection is built, comparison with the existing schemes is carried out; conditions for stability of the proposed difference scheme are obtained. Solutions of the convection-diffusion equation on the basis of the proposed difference scheme at various Peclet numbers are obtained.

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