Multiphysics simulation: Difference between revisions

Revision as of 07:34, 8 September 2020

Revision as of 02:02, 5 January 2021

Line 19:

=== Mathematical models ===

{{see also|Mathematical models}}

A mathematical model is essentially a set of equations. The equations can be divided into three categories{{which|date=October 2019}} according to the nature and intended role.: Thegoverning firstequations, categoryauxiliary isequations governingand equationsboundary / initial conditions. A governing equation describes the major physical mechanisms and process without further revealing the change and nonlinearity of the material properties. For example, in a heat transfer problem, the governing equation could describe a process in which the thermal energy (represented using temperature or enthalpy) at an infinitesimal point or a representative element volume is changed due to energy transferred from surrounding points via conduction, advection, radiation, and internal heat sources or any combinations of these four heat transfer mechanisms as the following equation:<ref name=":0" />

<math>{\underbrace{\frac{\partial u}{\partial t} }_{{\rm Accumulation}}\underbrace{+\nabla \cdot \left(uv\right)}_{{\rm Advection}}\underbrace{-\nabla \cdot \left(D\nabla u\right)}_{{\rm Diffusion\; }\left({\rm Conduction, Dispersion}\right)}=\underbrace{Q}_{{\rm Source}}}