Multiphysics
Table of Contents
1. Overview
Multiphysics studies several computer models of physical phenomena, coupled to each other. Apparently it is a contraction of "Multi-scale physics". For our interests, the atmosphere coupled to ocean dynamics, factoring in thermodynamic heat transfer. More generally, we have Constituent systems which are coupled together; the code is organized to reflect this, using a Coupler pattern (a Mediator with delusions of grandeur). The only person who has defined terms to describe multiphysics appears to be J. Walter Larson in his article "Ten organising principles for coupling in multiphysics and multiscale models".
COMSOL seems to be a proprietary company with some kind of software, claiming to be the "alpha and omega" on multiphysics. I never heard of the term before stumbling across them by accident.
1.1. A Grocery List of Definitions
A Constituent \(\mathcal{C}\) is characterized by a "model" \(\mathcal{M}\) which solves its equations of motion on its domain \(\Gamma\) to calculate its State \(\mathcal{U}\).
The state is updated using the current model's state and a set of Input Variables \(\mathcal{V}\). The Output Variables \(\mathcal{W}\) are computed from \(\mathcal{U}\)
The input and output variables \(\mathcal{V}\) and \(\mathcal{W}\) are the only data connections of a constituent system to the "outside world", and are defined on the Boundary Domain \(\partial\Gamma\) (or some subset of it).
For example, the Earth's atmosphere has \(\Gamma\) be the region between the surface of the Earth and the "top of the atmosphere". So usually it's the difference between two closed balls \(\Gamma=B^{3}_{\text{atm}}\setminus B^{3}_{\text{earth}}\). The standard mesh for numerically computing finite differences is a \(64\times128\times26\) grid; this could be taken as the domain for a numerical approximation to the Earth's atmosphere.
Two constituents \(\mathcal{C}_{i}\) and \(\mathcal{C}_{j}\) are Coupled if
- Have some common intersection of their domains: \(\Gamma_{i}\cap\Gamma_{j}\neq\emptyset\), and
- Outputs from one can serve as inputs to the other,
in at least one of the following senses:
- One constituent's outputs overlap the other's inputs: \(\mathcal{W}_{j}\cap\mathcal{V}_{i}\neq\emptyset\), and/or \(\mathcal{V}_{j}\cap\mathcal{W}_{i}\neq\emptyset\); or
- The inputs \(\mathcal{V}_{i}\) can be computed from the other's outputs \(\mathcal{W}_{j}\) (or \(\mathcal{V}_{j}\) can be obtained from \(\mathcal{W}_{i}\)).
We then describe a multiphysics system as a finite collection of constituents \(\mathcal{C}_{i}\) (where \(i=1,\dots,N\)), which are usually coupled together somehow.
The difficulty stems from time-evolution. For explicit finite difference schemes, it's straightforward…usually. But for implicit finite difference schemes, it's a nightmare of sharing "the current guess of the next iterative state's values".
2. References
- DWM Rouson, H. Adalsteinsson, and J. Xia, "Design patterns for multiphysics modeling in Fortran 2003 and C++". ACM Transactions on Mathematical Software 37, 1(2010) doi:10.1145/1644001.1644004.
- Damian Rouson, Jim Xia, Xiaofeng Xu, Scientific Software Design: The Object-Oriented Way. Cambridge University Press, 2011.
- J. Walter Larson,
"Ten organising principles for coupling in multiphysics and multiscale models".
ANZIAM 48 (2009) Eprint - Gang Lu, Efthimios Kaxiras,
"Overview of Multiscale Simulations of Materials".
PDF, 33 pages. - David Keyes and many friends,
"Multiphysics simulations: Challenges and opportunities".
Internat. J. of High Performance Comp. App. 27, no.1 (2013) pp.4-83, PDF
2.1. In Climate Science
A review of multiphysics, as applied to meteorology and climate science, may be found in:
- R. Klein, S. Vater, E. Paeschke, and D. Ruprecht, "Multiplescales methods in meteorology". In: Steinrück H. (eds) Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances. CISM Courses and Lectures, vol 523. Springer Verlag, 2011, pp.127–196, doi:10.1007/978-3-7091-0408-8_5