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.
|Keywords||hyperbolic conservation laws, convection, finite-volume method, immersed-boundary method, embedded boundaries, dimensional splitting|
|THEME||Life Sciences (theme 5), Energy (theme 4)|
|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.