Multiscale Modeling is touched on in Fluid Mechanics but here, will traverse the scale through the lectures.
Ab Inito Methods derive materials properties from first principals or wave equation
Pros
electronic and structural behavior and properties
bond breaking and formation in chemical reaction
can systematically improve results to prove quality
in principal, can obtain exact properties
Cons
very small systems, ~O(10E2) atoms
very small timescales, ~O(10E-12) or pico seconds
numerically expensive on even super computers of ~O(10E15) flops
Atomistic Methods is the range of semi classical statistical mechanics for thermodynamic and transport properties
Pros
Systems larger on scale of ~O(10E4) and ~O(10E6) atoms
Larger timescales of ~O(10E-9) to O(10E-6) second
Cons
results depend on force field used
Transport properties dependent on macroscale conditions which affect physical processes
Mesoscale methods is a level of simplification treating clusters of atoms as blobs of matter. An abstraction which allows for some computational savings by calculation as entities moving through a potential field.
Pros
Study structural features of complex systems on size ~O(10E8) or more
Dynamic processes on the order of a second
Cons
Mostly only qualitative tendencies, with quality difficult to ascertain
Approximations limit insight
Continuum Methods: assume matter can be treated as field quantity which changes continuously. Solve balance equations, per FEM and CFD.
Pro: rest of the time lengthscale diagram is accessible
Con Require viscosity, diffusion coefficients, and other transport properties
Upscaling is the using a lower lengthscale information to inform the properties of higher length scales in a deductive approach
Downscaling is using higher scale, often experimental information, to inform lower order parameters. More difficult due to non-uniqueness.
Lecture 2: Ab Inito Principals, Fundamentals
Lecture 3: Ab Inito and Density Functional Theory, Part 1
