A new approach for conjugate heat transfer problems using immersed boundary method for curvilinear grid based solvers

Use of immersed boundary method (IBM) based techniques have helped considerably in easing the grid generation process in flows involving complex geometries and/or large boundary movements. Body fitting grid based techniques still, however, are advantageous in terms of accuracy and efficiency. In this work, we have developed an IBM scheme applicable to curvilinear coordinates, aiming at taking advantage of both the methodologies. The framework uses efficient algorithms for search, locate, and interpolate operations. A new method of implementing the conjugate heat transfer (CHT) boundary condition is proposed which is a direct extension of the method used for other boundary conditions and does not involve any complex interpolations like previous CHT implementations using IBM. The developed scheme is shown to be applicable to complex geometries on curvilinear grids, while also being very efficient, consuming less than 1% of the total simulation time per time-step. Very good scalability on massive computations is demonstrated using strong scaling study up to 1024 cores. Detailed code verification process is undertaken to show that the method is second-order accurate for both the velocity and temperature fields for all the boundary conditions considered. Further, validation studies involving uniform flow over stationary and oscillating cylinders are carried out to demonstrate the accuracy of the developed method. Lastly, simulations are performed to study flow and conjugate heat transfer through thick-walled micro-channels using body-fitted background grids and the results are shown to be in excellent agreement with previously published results.