ИСТИНА

The present paper addresses computational mechanics of heterogeneous media. Using the term “heterogeneous” we mean non-uniform continuum that consists of several materials (components) with different physical and mechanical properties. Each component can be in either gas, liquid, or solid phase. Our interest lies in the range of strong dynamical processes that are accompanied by large deformations. Therefore we develop the Eulerian approach where the interface between different materials is captured on a stationary spatial grid with a volume-of-fluid interface tracking algorithm. Spatial distributions of the materials are defined by corresponding volume fractions, and multimaterial dynamics is modeled by constructing an effective single phase continuum in which density, pressure, internal energies are defined by averages of the individual material properties. In this method computational cells can represent pure materials, but can also be mixed and represent several materials. To split the mixed cell and determine parameters of the individual phases, several closure models are examined. Numerical dissipation of Eulerian methods inevitable will smear interfaces, which will result in material-to-material contaminations and appearing expanded regions of mixed cells. This is pure numerical effect that can mispresent the simulated problem. To reduce this negative numerical effect, we propose a method that allows us to approximately resolve the sub-cell interface structure and use this additional data to more accurate calculate the numerical flux at cell faces. We demonstrate that this approach can remarkably narrow the interface smearing zone, and reduce it to a few computational cells. The method is developed for 2D and then extended to 3D problems. Its accuracy and robustness are demonstrated on simulating Richtmyer — Meshkov instability, triple point problem, and high speed impact of slightly stratified materials. To enhance the interface capturing property of the method proposed we implement also the technology of adaptive mesh refinement (AMR). This is carried out for the Cartesian grids. The problem to be computed is initially set up on a Cartesian regular grid which is then locally adapted to the material interfaces by recursively dividing the cells containing the interface in two in each direction. The calculation is executed with this grid accompanied by the procedures of grid refinement/coarsening so that mixed cells always correspond to the lowest level of adaptation with minimal space size. The results will be shown at the Conference that are expected to demonstrate the ability of the AMR implementation to produce a very high (pixel/voxel-type) resolution of material interfaces.