Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods |
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Authors: | Juan Carlos De los Reyes,Sergio Gonzá lez Andrade |
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Affiliation: | Research Group on Optimization, Department of Mathematics, EPN Quito, Ecuador |
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Abstract: | This paper is devoted to the numerical simulation of two-dimensional stationary Bingham fluid flow by semismooth Newton methods. We analyze the modeling variational inequality of the second kind, considering both Dirichlet and stress-free boundary conditions. A family of Tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified. By using Fenchel’s duality, optimality systems which characterize the original and regularized solutions are obtained. The regularized optimality systems are discretized using a finite element method with (cross-grid P1)-Q0 elements for the velocity and pressure, respectively. A semismooth Newton algorithm is proposed in order to solve the discretized optimality systems. Using an additional relaxation, a descent direction is constructed from each semismooth Newton iteration. Local superlinear convergence of the method is also proved. Finally, we perform numerical experiments in order to investigate the behavior and efficiency of the method. |
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Keywords: | 76A10 35R35 47J20 65K10 47A52 90C46 90C53 |
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