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Creators/Authors contains: "Scott, L. Ridgway"

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  1. ; (, Advances in Computational Science and Engineering)
    We explore the possibility of simulating the grade-two fluid model in a geometry related to a contraction rheometer, and we provide details on several key aspects of the computation. We show how the results can be used to determine the viscosity ν from experimental data. We also explore the identifiability of the grade-two parameters α1 and α2 from experimental data. In particular, as the flow rate varies, force data appears to be nearly the same for certain distinct pairs of values α1 and α2; however, we determine a regime for α1 and α2 for which the parameters may be identifiable with a contraction rheometer. 
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  2. ; (, Advances in Computational Science and Engineering)
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  3. ; (, Partial Differential Equations and Applications)
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  4. ; (, ESAIM: Mathematical Modelling and Numerical Analysis)
    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. 
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