A decoupled scheme for a single-phase model in ferrohydrodynamics
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Abstract
In this Ph.D. research, we propose numerical approximations of a simplified model for single phase ferrofluid flow, which consists of the Navier–Stokes equations coupled with the Poisson equation. Using several spatial and temporal discretization techniques for the weak formulation, we construct a fully discrete finite element scheme with linearizations to solve the highly nonlinear and coupled multiphysics PDE system in ferrohydrodynamics (FHD). Also, we obtain a decoupled numerical scheme to solve the system more efficiently. Furthermore, we provide numerical experiments to demonstrate the stability and accuracy capabilities of the numerical schemes for both coupled and decoupled systems. Finally, we study the existence and uniqueness of the the decoupled scheme for the linearized system, and derive optimal error estimates for fully discretized schemes. We also investigated well-posedness, stability and the convergence analysis of the fully discretized decoupled scheme of the FHD model under reasonable assumptions.
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Introduction and literature review -- Preliminaries -- Coupled scheme for a single-phase model in FHD -- A decoupling scheme -- Stability and convergence -- Conclusion
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Ph.D. (Doctor of Philosophy)