Conservative Front Tracking: the Algorithm, the Rationale and the API
Vol. 11 No. 1 (2016) P.115~P.130
A conservative algorithm for front tracking, previously proposed, is developed here
in detail. Conservation follows from general ideas of numerical analysis. Portions of the
algorithm are higher order.
Front tracking is well suited to the study of problems in turbulent mixing, in that
it controls excess numerical species concentration diffusion, normally present in Eulerian finite difference codes. Conservative tracking is important to prevent a gradual drift away from correct mass balances.
We propose an Application Programming Interface (API) to mediate the insertion
of front tracking into an external physics code. The main requirement upon a client code
imposed by the API is a front-aware interpolation function, which is used to construct two sided states at each front point. These states are defined by interpolation or extrapolation
from interior states on each side of the front. Using these, we define a time integration for front points, and a conservative time integration for interior (grid cell average solution values). We define this first for cells not cut by the front and then for cut cells also. Reference implementations of client functions will be provided for regular grid client codes.
Front Tracking, numerical diffusion.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 76F35, 76F65.
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Revised : 2015-07-15