A two-dimensional embedded-boundary method for convection problems with moving boundaries

In this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes in the immediate neighbourhood indirectly accommodate effects of the boundary conditions valid on the moving (immersed-)body. Over the majority of the domain, where these boundary conditions have ‘no’ effect, the fluxes are computed using standard schemes. We employ the method of lines, with higher-order spatial discretizations and the explicit Euler scheme for the time integration. To validate the method, two cases, a rectilinear discontinuity of arbitrary orientation, moving in a uniform two-dimensional flow-field, and a cylindrical discontinuity of arbitrary initial location, moving in a circular flow-field, are considered. The simulations show promising, globally accurate solutions. It is anticipated that the algorithm can be used for 2D Euler flows, which we foresee to consider next.