We propose to develop a new capability based on high-order high-resolution schemes to simulate shock-turbulence interactions and multi-material mixing in planar and spherical geometrical configurations and study the turbulent RT and RM mixing. These problems are of relevance to ICF capsule implosion and supernovae explosions.The project also involves the development of novel sub-grid models for shock-turbulence interaction and multi-material mixing and its validation using the DNS data. more.....