Roller Numerical Methods

From CIRPwiki
Revision as of 20:12, 31 July 2014 by (username removed) (Created page with " The surface roller transport equation is solved in CMS-Wave using a finite difference method. The source terms are calculated at the grid cell centers. The advective or trans...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

The surface roller transport equation is solved in CMS-Wave using a finite difference method. The source terms are calculated at the grid cell centers. The advective or transport term is approximated using either the first-order or second-order upwind finite difference scheme. The first order upwind scheme is given by

 

(1)

where and i and j indicate the position along either the rows or columns, and is the cell-center distance between adjacent cells in the jth direction and at position i. The second-order upwind scheme is given by

 

(2)

The surface roller calculation is achieved by setting the initial roller energy and time-stepping until the steady-state solution is reached. For simplicity, an explicit Euler scheme is used as follows {{Equation |3}}

where is the surface roller time step and is determined as is the cell size in the direction. The steady-state solution is typically reached after ~40-80 time steps and takes about 1-2 seconds to run on a desktop personal computer.


Documentation Portal