An explicit jump correction to the fast fictitious forces 3d Stokes solver

in preparation, June, 2007

Authors

• Liping Cheng
• Andreas Wiegmann

Abstract

Wiegmann[1] described the fast fictitious forces 3d Stokes solver for solving steady Stokes equations of the flows in porous media and geometrically complex materials. It is efficient and fast but implements the boundary conditions in tangential directions a half mesh width away from the correct locations. That is because in a MAC grid, the solid interfaces fall between grid cells for the variables in tangential directions and the no-slip boundary conditions are enforced a half mesh size inside the interfaces. To achieve higher accuracy, this paper adopts a jump correction scheme. The jump correction is derived by using Taylor expansions at the interface points. With a fictitious force term in normal direction and a jump correction term in tangential directions expressed as unknown body forces, the fast Fourier solver can still be utilized by extending all variables in the solid voxels. The Schur-complement formulation shows the resulting matrix is not symmetric. However, the jump corrected method obtains more accurate results, which is demonstrated by the Poiseuille flow in a channel and in a pipe.

BibTeX

 
@Article{ Cheng.Wiegmann06jumpCorrection, 
   title = { An explicit jump correction to the fast fictitious forces 3d Stokes solver }, 
   author = { Liping Cheng and Andreas Wiegmann },               
   note = { in preparation }, 
   month = jun, 
   year = 2007, 
} 

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This publication belongs to the project MultiFil.