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.
Additional Metadata
Keywords hyperbolic conservation laws, convection, finite-volume method, immersed-boundary method, embedded boundaries, dimensional splitting
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series CWI. Department of Modelling, Analysis and Computing [MAC]
Hassen, Y.J, & Koren, B. (2010). A two-dimensional embedded-boundary method for convection problems with moving boundaries. CWI. Department of Modelling, Analysis and Computing [MAC]. CWI.