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Multiscale modeling
Mathematical field / From Wikipedia, the free encyclopedia
Multiscale modeling or multiscale mathematics is the field of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids,[1][2][3] solids,[2][4] polymers,[5][6] proteins,[7][8][9][10] nucleic acids[11] as well as various physical and chemical phenomena (like adsorption, chemical reactions, diffusion).[9][12][13][14]
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An example of such problems involve the Navier–Stokes equations for incompressible fluid flow.
In a wide variety of applications, the stress tensor is given as a linear function of the gradient
. Such a choice for
has been proven to be sufficient for describing the dynamics of a broad range of fluids. However, its use for more complex fluids such as polymers is dubious. In such a case, it may be necessary to use multiscale modeling to accurately model the system such that the stress tensor can be extracted without requiring the computational cost of a full microscale simulation.[15]