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The free boundary algorithm can be easily extended for problems of higher dimensionality and we present results for a two-dimensional cell population balance model, which can exhibit an oscillatory behavior.
The flux equation, coupled with the mass transport and the fluid flow equations, allows for a natural implementation of an immersed boundary algorithm when the flux across the interfaces is proportional to the jump in concentration.
For the numerical simulation of the resulting formulation we developed a novel moving boundary algorithm which can efficiently treat the vastly different time scales that are inherent in this process.
It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (1998, J. Comput. Phys.147, 60) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative.
In this study, we compare the standard lacunarity algorithm with this new periodic boundary algorithm (a method often used in cellular automata modeling) to quantify the differences between the two approaches and to determine when the standard algorithm may suffer from deleterious effects.
Other studies have reported Stratus™ outer boundary algorithm errors of approximately 43% for both forms of AMD and 60% for NV-AMD.
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Moving wet dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions.
We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms.
When the multiresolution algorithms derived from univariate wavelet bi-frames are used as the boundary algorithms, it is desired that not only the scaling functions but also all framelets be symmetric.
The proposed approach belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary.
The proposed method belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary.
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Justyna Jupowicz-Kozak
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