Convective Coordinate Approach to Continuum Mechanics with Application to Electrodynamics.

摘要

The description of nonmechanical physical processes is simplified by using convective coordinates in place of reference coordinates for the mathematical characterization of physical boundaries. While the reference coordinates of standard continuum mechanics remain fixed in a single (possibly fictitious) configuration, convected coordinates move along with the particles of the simulation describing an evolving geometry as time progresses. This allows nonmechanical physical processes (such as electromagnetic fluxes) to be tracked easily even when introducing discontinuities in the continuum. Moreover, because the convective description refers to the evolving physics in real time, it may be used to evaluate the fidelity of physical models in different reference frames. To demonstrate the utility of these coordinates and investigate an important application, Maxwell's equations of electrodynamics are formulated in the convective system.