Articles written in Sadhana

    • A monolithic finite-element formulation for magnetohydrodynamics


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      This work develops a new monolithic strategy for magnetohydrodynamics based on a continuous velocity–pressure formulation. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite-element framework. The velocity and pressure interpolations are chosen so that they satisfy the Babuska–Brezzi (BB) conditions. In most of the existing formulations, a stabilized formulation is used that requires a stabilization term, and some associated mesh-dependent parameters that need to be adjusted. In contrast, no such parameters need to be adjusted in the current formulation, making it more user-friendly and robust. Both transient and steady-state formulations are developed for two- and three dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergenceis achieved within each time (or load) step, while the stable nature of the interpolations used ensures that no instabilities arise in the solution. An existing analytical solution is corrected. The coarse mesh accuracy is shown to be better compared with other existing strategies in several benchmark problems, showing that the developed formulation is both robust and efficient.

    • A monolithic finite element strategy for conjugate heat transfer


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      Motivated by several applications such as thermal management of electronic components, the design and modeling of heat exchangers, etc. this work presents an efficient monolithic finite element strategy for solving thermo-fluid-structure interaction problems involving a compressible fluid and a structure undergoing small deformations. This formulation uses displacement variables for the structure and velocity variables for the fluid, with no additional variables required to ensure traction, velocity, temperature and heat flux continuity at the fluid-structure interface. The use of an exact tangent stiffness matrix ensures a quadratic rate of convergence within each time step. The robustness and good performance of the method is demonstrated by applying the proposed strategy to a wide spectrum of problems pertaining to steady/transient, two/three-dimensional/ axisymmetric problems involving conjugate heat transfer. In particular, it is shown that the proposed formulation yields good results even when the fluid is almost incompressible.

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