Implementation of Immersed Boundary Method in WENO Scheme to Simulate Shock-Structure Interaction Available to Purchase

In the present work, a sharp interface immersed boundary method using ghost-cells is implemented in a traditional 5th-order WENO scheme for shock capturing. To avoid non-physical negative density and pressure involved in high order conservative schemes, a cut-off flux limiter is introduced to enforce the positivity-preserving property, which allows to simulate the flow near vacuum and with strong discontinuities. The combined approach was first benchmarked by a steady oblique shock reflection problem with an exact solution from the oblique shock theory. Then, the algorithm was tested for singularity treatment by another classical problem of shock interaction with a forward facing step. For problems with moving boundaries, the new approach was validated against well-tested numerical solutions of a prescribed moving cylinder problem and a shock-lifting-off-cylinder problem. The agreement in all the benchmark studies shows the accuracy and capability of the current algorithm, in its simple form, to simulate the shockwave interacting with stationary obstacles or moving structures, where the structures′ motion can be either prescribed or determined by fully-coupled dynamics with surrounding flows. Finally, the approach was applied to investigate the impact of shock waves on a deformable body modeled by spring-linked plates, with different spring constants being considered.