This initialization phase also specifies the computational domain and possibly some termination condition for the time loop. The MMSF is a theoretical and practical way to model, describe and simulate multi-scale, multi-science phenomena. By adhering to a single framework, not tied to a specific discipline, groups of researchers ensure that their respective contributions may cooperate with those of others.
General methodologies
A more rigorous approach is to derive the constitutive relation frommicroscopic models, such as atomistic models, by taking thehydrodynamic limit. For simple fluids, this will result in the sameNavier-Stokes equation we derived earlier, how to hire a software developer now with a formula for\(\mu\) in terms of the output from the microscopic model. But forcomplex fluids, this would result in rather different kinds of models.This is one of the starting points of multiscale modeling.
Averaging methods
- Various tricks are then used to entice the microscalesimulations on small domains to behave like a full simulation on thewhole domain.
- Biomedical applications, where biology is coupled to fluid mechanics, are an illustration of a multi-scale, multi-science problem.
- In this paper, we have formalized the process of multi-scale modelling and simulation in terms of several well-defined steps.
- Vanden-Eijnden, “A computational strategy for multiscale chaotic systems with applications to Lorenz 96 model,” preprint.
- If these two processes are decomposed, a vegetation submodel could take a grid with the vegetation per point and a fire submodel only needs a grid with points marked as able to burn or not.
- The above features (respective position in the SSM and domain relation) offer a way to classify the interactions between two coupled submodels.
By repeating the analysis with other peaks, other periodicities such as the out-of-plane spacing can be measured in the same way. The second application we briefly discuss here is the suspension fluid example. It is characterized by temporal and spatial scale separation. A hard sphere suspension model is used on the fine scale, an advection–diffusion model on the meso-scale, and a non-Newtonian fluid dynamics model on the coarse-scale 20.
Sequential multiscale modeling
In the heterogeneous multiscale method (E and Engquist, 2003), one startswith a preconceived form of the macroscale model with possible missingcomponents, and then estimate the needed data from the microscalemodel. In the multiscale approach, one uses a variety of models at differentlevels of resolution and complexity to study one system. Thedifferent models are linked together either analytically ornumerically. For example, one may study the mechanical behavior ofsolids using both the atomistic and continuum models at the same time,with the constitutive relations needed in the continuum model computedfrom Multi-scale analysis the atomistic model.