Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method

Authors:
Kazufumi Ito;Zhilin Li
Affiliations:
Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, North Carolinia 27695. kito@math.ncsu.edu;Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, North Carolinia 27695. zhilin@math.ncsu.edu
Venue:
Journal of Scientific Computing
Year:
2003

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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.