Multiscale modeling

Multiscale modeling or multiscale mathematics is the <a href="/facts/Branches_of_science/tKykGyUj">field</a> of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids, solids, polymers, proteins, <a href="/facts/Nucleic_acids/2tTgcI0v">nucleic acids</a> as well as various physical and chemical phenomena (like adsorption, chemical reactions, <a href="/facts/Diffusion/KbAxroBa">diffusion</a>).
An example of such problems involve the <a href="/facts/Navier%25E2%2580%2593Stokes_equations/48pQugEa">Navier–Stokes equations</a> for incompressible fluid flow.

 
 
 
 
 
 
 
 
 ρ
 
 0
 
 
 (
 
 ∂
 
 t
 
 
 
 u
 
 +
 (
 
 u
 
 ⋅
 ∇
 )
 
 u
 
 )
 =
 ∇
 ⋅
 τ
 ,
 
 
 
 
 ∇
 ⋅
 
 u
 
 =
 0.
 
 
 
 
 
 
 {\displaystyle {\begin{array}{lcl}\rho _{0}(\partial _{t}\mathbf {u} +(\mathbf {u} \cdot \nabla )\mathbf {u} )=\nabla \cdot \tau ,\\\nabla \cdot \mathbf {u} =0.\end{array}}}

In a wide variety of applications, the stress tensor 
 
 
 
 τ
 
 
 {\displaystyle \tau }
 
 is given as a linear function of the gradient 
 
 
 
 ∇
 u
 
 
 {\displaystyle \nabla u}
 
. Such a choice for 
 
 
 
 τ
 
 
 {\displaystyle \tau }
 
 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.

Multiscale modeling open-in-new

Multiscale modeling