Jump‐reduced immersed boundary method for compressible flow

Abstract

SummaryThe main challenge of the immersed boundary approach is the proper enforcement of boundary conditions on the body interface without any spurious oscillations, which are induced by the nongrid‐conforming boundary configuration. In this study, a new sharp interface ghost‐cell immersed boundary method (IBM) is proposed for obtaining solutions near the immersed boundary with a high order of accuracy. The main idea is “jump‐reduction” instead of jump‐correction across the boundary interface by combining the ghost‐cell method with the flow reconstruction method. In the proposed IBM, the unknown values at the three points, that is, boundary points, ghost cell, and flow field reconstruction point are solved simultaneously using equations formulated by the moving least‐squares interpolation method. It is a hybrid of ghost‐cell and flow reconstruction methods, correlated with interface values, which result in a reduced jump‐discontinuity. In addition, a discontinuity‐distinguishing algorithm is introduced so that the low‐order method is applied only to the discontinuous or non smooth region, while the current high‐order method is applied elsewhere. Reduced jump‐discontinuity of the proposed IBM has been verified in both subsonic and supersonic flow using fundamental benchmark problems. We observed that the reduced jump‐discontinuity does not hamper the mass conservation and shows even better conservation property than conventional methods due to the nonoscillatory performance in smooth regions. The numerical results further confirm the ability of the proposed IBM to solve complex flow physics with high‐order accuracy and improved stability.

Cell‐based hybrid adaptive mesh refinement algorithm for immersed boundary method

“…Also, the high‐order IBM extensions were demonstrated through the double Mach reflection problem. The validation and performance of a uniform grid solver with IBM were extensively studied in our previous works 2,3 . The proposed AMR method results are compared with the validated uniform grid results.…”

“…The immersed boundary method (IBM), a type of non‐conformal grid method, can handle complex geometries in the Cartesian grid system owing to its flexibility in treating boundary conditions. A detailed classification of IBM and the pros and cons of each method were discussed in our previous papers 2,3 . An inherent inability to cluster grids in the vicinity of the immersed boundary is one of the IBM's major drawbacks 4 .…”

Developing an immersed boundary method for compressible flow

“…Non‐conforming grid methods, such as cut‐cell methods and immersed boundary methods (IBM), do not require remeshing, which saves computational time [1, 2]. However, these methods require more sophisticated techniques to apply boundary conditions at non‐grid‐aligned boundaries.…”