Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D

In this paper, we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space. Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions. We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes. The method is an extension of the inverse Lax-Wendroff (ILW) procedure in our works (Cheng et al., Appl Math Mech (Engl Ed) 42: 841–854, 2021; Liu et al.) for 2D problems. Different from the 2D case, the local coordinate rotation in 3D required in the ILW procedure is not unique. We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation, ensuring the method is feasible and valid. Both translation and rotation of the body are taken into account in this paper. In particular, we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition, which plays a key role in the proposed algorithm. Numerical simulations on the cylinder and sphere are given, demonstrating the good performance of our numerical boundary treatments.