A level set approach to Eulerian–Lagrangian coupling

We present a numerical method for coupling an Eulerian compressible flow solver with a Lagrangian solver for fast transient problems involving fluid–solid interactions. Such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different (Eulerian or Lagrangian) schemes. The algorithm we propose employs standard integration of the Eulerian solution over a Cartesian mesh. To treat the irregular boundary cells that are generated by an arbitrary boundary on a structured grid, the Eulerian computational domain is augmented by a thin layer of Cartesian ghost cells. Boundary conditions at these cells are established by enforcing conservation of mass and continuity of the stress tensor in the direction normal to the boundary. The description and the kinematic constraints of the Eulerian boundary rely on the unstructured Lagrangian mesh. The Lagrangian mesh evolves concurrently, driven by the traction boundary conditions imposed by the Eulerian counterpart. Several numerical tests designed to measure the rate of convergence and accuracy of the coupling algorithm are presented as well. General problems in one and two dimensions are considered, including a test consisting of an isotropic elastic solid and a compressible fluid in a fully coupled setting where the exact solution is available.