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Title: An algorithm for the grade-two rheological model
We develop an algorithm for solving the general grade-two model of non-Newtonian fluids which for the first time includes inflow boundary conditions. The algorithm also allows for both of the rheological parameters to be chosen independently. The proposed algorithm couples a Stokes equation for the velocity with a transport equation for an auxiliary vector-valued function. We prove that this model is well posed using the algorithm that we show converges geometrically in suitable Sobolev spaces for sufficiently small data. We demonstrate computationally that this algorithm can be successfully discretized and that it can converge to solutions for the model parameters of order one. We include in the appendix a description of appropriate boundary conditions for the auxiliary variable in standard geometries.  more » « less
Award ID(s):
2011519
PAR ID:
10343111
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ESAIM: Mathematical Modelling and Numerical Analysis
Volume:
56
Issue:
3
ISSN:
2822-7840
Page Range / eLocation ID:
1007 to 1025
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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