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GDP is based on creating an artificial and fictitious boundary, assuming that if you produce what you consume, you do not produce.
In this paper, we investigate the numerical simulation of particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [S.
Turek, D.C. Wan, L.S. Rivkind, The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations.
A correction to the Cauchy Born rule is introduced in the overlap region to minimize fictitious boundary effects.
The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series.
Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS).
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The numerical studies of both open and closed fictitious boundaries are considered.
Our strategy is based on typical domain splitting algorithm where the initial mesh is split into parts that are then meshed in parallel while the fictitious boundaries between parts are kept unchanged.
Since the MFS source points placement here is not trivial due to the unknown boundary, we employ an adaptive technique to choose a sub-optimal arrangement of source points on various fictitious boundaries.
Application of the optimized templates to both the linear convection and Burgers equations at a fictitious non-periodic boundary showed major reductions of the predictive error.
The Burton Miller method is used to filter out the fictitious eigenfrequencies of the boundary integral formulations.
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