Diffuse interface immersed boundary/finite volume framework for compressible viscous flows

The computation of compressible viscous flows is relevant to aeronautical and space applications which also involve complex geometries. Some of the applications that are of interest include design of scramjet intakes and predictions of heat transfer in re-entry configurations. The latter is signicant from the viewpoint of design of thermal protection systems while the former is key for high-speed transport. The use of computational fluid dynamics (CFD) has gained prominence over the last two decades and offers a viable alternative in scenarios where experiments are difficult, costly and even impossible to perform. Among the several possible numerical frameworks, the use of immersed boundary (IB) methods is fast gaining favour among the scientic community, largely due to its simplicity and speed without unduly compromising on the accuracy of the solution. However, the IB frameworks are not free of problems either and have not been employed as much in the compressible regime in comparison to studies in the incompressible domain. The major advantage of IB frameworks are that they work with a fixed background mesh (typically Cartesian) which allows handling complex geometries (both stationary and moving) with relative ease while also signicantly reducing the cost associated with unstructured mesh generation. This assumes importance in the early design phase where minor changes in design would otherwise necessitate re-meshing with conventional CFD approaches and for a large number of parametric studies lead to a large turnaround time. The use of IB frameworks would allow for shorter turnaround times and fast computation but their accuracy and robustness for high-speed compressible flows need to be studied in greater detail. While these frameworks work with non-conformal meshes into which the bodies are "embedded", the means of enforcing the boundary conditions (BCs) distinguishes different IB approaches. While the sharp interface IB approaches that directly enforce the BCs on the surface of the geometry are most favoured, these are fraught with issues of spurious force oscillations and more recently, anomalous predictions of heat transfer in hypersonic flows. The diffuse interface IB approaches smear the geometric interface over a few cell widths but have shown comparable performance as their sharp-interface counterparts, atleast for a wide variety of incompressible flow problems, with signicant reduction in SFOs as well. However, there have neither been systematic studies comparing the sharp and diffuse interface IB approaches nor efforts to employ the class of diffuse interface IB approaches for high-speed viscous flows with an emphasis on near-wall heat transfer and skin friction predictions.