Numerical simulations and global existence of solutions of two-dimensional flows of fluids with pressure- and shear-dependent viscosities Conference Paper

abstract

• There is a considerable amount of experimental evidence that unequivocally shows that there are fluids whose viscosity depends on both the mean normal stress (pressure) and the shear rate. Recently, global existence of solutions for the flow of such fluids for the three-dimensional case was established by Mlek, Neas and Rajagopal. Here, we present a proof for the global existence of solutions for such fluids for the two-dimensional case. After establishing the global-in-time existence, we discretize the equations via the finite element method, outline the Newton type iterative method to solve the non-linear algebraic equations and provide numerical computations of the steady flow of such fluids in geometries that have technological significance. 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

authors

• Rajagopal, Kumbakonam

published proceedings

• MATHEMATICS AND COMPUTERS IN SIMULATION

author list (cited authors)

• Hron, J., Malek, J., Necas, J., & Rajagopal, K. R.

citation count

• 35

complete list of authors

• Hron, J||Malek, J||Necas, J||Rajagopal, KR

publication date

• January 2003

publisher

• Elsevier  Publisher

published in

• Mathematics and Computers in Simulation  Journal

keywords

• Finite Element Discretization
• Global-in-time Existence
• Incompressible Fluid
• Newton Iterative Solver
• Numerical Simulation
• Pressure-dependent Viscosity
• Shear-dependent Viscosity
• Weak Solution

Digital Object Identifier (DOI)

• 10.1016/S0378-4754(02)00085-X

start page

• 297

end page

• 315

volume

• 61

issue

• 3-6

URL

• http://dx.doi.org/10.1016/s0378-4754(02)00085-x