Finite element methods for the simulation of incompressible powder flow. Ouazzi, a., Turek, S., & Hron, J. Communications in Numerical Methods in Engineering, 21(10):581-596, 6, 2005.
abstract   bibtex   
Unlike fluids, flowing powders do not exhibit viscosity such that a Newtonian rheology cannot accurately describe granular flow. Assuming that the material is incompressible, dry, cohesionless, and perfectly rigid-plastic, and based on continuum theories, generalized Navier-Stokes equations ('Schaeffer Model') have been derived where the velocity gradient has been replaced by the shear rate, and the viscosity depends on pressure and shear rate which leads to mathematically complex problems. In this note we present numerical algorithms to approximate these highly non-linear equations based on finite element methods; A Newton linearization technique is applied directly to the corresponding continuous variational formulations. The approximation of incompressible velocity field is treated by using stabilized nonconforming Stokes elements and we use a pressure Schur complement smoother as defect correction in a direct multigrid approach to solve the linear saddle-point problems with high numerical efficiency. The results of several computational experiments for prototypical flow configurations are provided. Copyright © 2005 John Wiley & Sons, Ltd.
@article{
 title = {Finite element methods for the simulation of incompressible powder flow},
 type = {article},
 year = {2005},
 identifiers = {[object Object]},
 keywords = {Non-conforming FEM,Powder flow,Schaeffer model},
 pages = {581-596},
 volume = {21},
 websites = {http://doi.wiley.com/10.1002/cnm.775},
 month = {6},
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 abstract = {Unlike fluids, flowing powders do not exhibit viscosity such that a Newtonian rheology cannot accurately describe granular flow. Assuming that the material is incompressible, dry, cohesionless, and perfectly rigid-plastic, and based on continuum theories, generalized Navier-Stokes equations ('Schaeffer Model') have been derived where the velocity gradient has been replaced by the shear rate, and the viscosity depends on pressure and shear rate which leads to mathematically complex problems. In this note we present numerical algorithms to approximate these highly non-linear equations based on finite element methods; A Newton linearization technique is applied directly to the corresponding continuous variational formulations. The approximation of incompressible velocity field is treated by using stabilized nonconforming Stokes elements and we use a pressure Schur complement smoother as defect correction in a direct multigrid approach to solve the linear saddle-point problems with high numerical efficiency. The results of several computational experiments for prototypical flow configurations are provided. Copyright © 2005 John Wiley & Sons, Ltd.},
 bibtype = {article},
 author = {Ouazzi, a. and Turek, Stefan and Hron, J.},
 journal = {Communications in Numerical Methods in Engineering},
 number = {10}
}
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