  In this paper we develop a conservative sharp-interface method dedicated to
simulating multiple compressible fluids. Numerical treatments for a cut cell
shared by more than two materials are proposed. First, we simplify the
interface interaction inside such a cell with a reduced model to avoid explicit
interface reconstruction and complex flux calculation. Second, conservation is
strictly preserved by an efficient conservation correction procedure for the
cut cell. To improve the robustness, a multi-material scale separation model is
developed to consistently remove non-resolved interface scales. In addition,
the multi-resolution method and local time-stepping scheme are incorporated
into the proposed multi-material method to speed up the high-resolution
simulations. Various numerical test cases, including the multi-material shock
tube problem, inertial confinement fusion implosion, triple-point shock
interaction and shock interaction with multi-material bubbles, show that the
method is suitable for a wide range of complex compressible multi-material
flows.
