Analysis of coupled grid methods for solving convection-diffusion equations

TL;DRAbstract

The error behavior of finite difference discretization schemes has been researched. Starting from the onedimensional case, where two particles of a fluidized bed were taken, the diffusion equation was numerically solved on a single grid as reference. Then the diffusion equation, a model equation for the real problem, was solved on a separated grids setup, where the grid spacing of the grid adjacent to the particles is relatively fine and the other grid relatively coarse. The main problem is the communication/coupling between these two grids. The research question of this report is: Is it possible to couple the two grids in a way that the numerical solution on the coupled grids has the same order of error behavior as the numerical solution on a single grid? If this is possible what are the minimal conditions for the coupling strategy? Different strategies of this coupling are proposed. The order of the error of the numerical solution was first estimated by Richarson error estimation and

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