Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method |
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Authors: | Kazufumi Ito Zhilin Li |
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Affiliation: | (1) Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, North Carolinia, 27695 |
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Abstract: | Many applications lead to a nonlinear elliptic interface problem in which the discontinuous coefficient depends on the solution and the material properties. A finite difference method based on Cartesian grids and the maximum principle preserving immersed interface method is proposed for the nonlinear elliptic interface problems discussed in this paper. Numerical experiments against the exact solutions reveal that our method is nearly second order accurate in the infinity norm. The method is applied to study the magneto-rheological field-responsive fluids that contain iron particles. Numerical experiments are performed against the results from the literature. |
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Keywords: | non-linear interface problem magneto-rheological fluid maximum principal preserving scheme immersed interface method level set method substitution method |
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