A simple immersed boundary method for non-Cartesian grids and conjugate heat transfer

What is it about?

Immersed boundary methods (IBM) help simplify handling of complex shapes in computational fluid dynamics. We go a step above most other IBM implementations by combining it with non-Cartesian background grid - this gives us the best of both worlds - the efficiency on non-Cartesian grids for macro geometrical features, and the ease of handling complex micro geometries using IBM. Also, we present for the first time a second-order accurate approach to handle conjugate heat transfer problems.

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Why is it important?

Our proposed proposed is novel and easy to implement, for all the boundary conditions. Non-Cartesian grid based IBM implementations are rare in the literature and our paper presents a straight-forward way to attack this problem. The conjugate heat transfer BC has been considerably simplified and yet yields, for the first time, a second-order accuracy.