A conservative interface-interaction method for compressible multi-material flows

Abstract

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.

Phenomenology of bubble-collapse-driven penetration of biomaterial-surrogate liquid-liquid interfaces

“…Heat conduction is considered as negligible due to the small physical timescales (in the range of microseconds), and mass diffusion and phase transfer also can be neglected [6]. The employed sharp-interface method [21] can handle complex interface topology changes.…”

“…is used to reconstruct the global level-set function [32,33]. Note, for more than two phases present in a computational cell, interface advection is non-trivial since all interactions need to be considered [21]. The interface segments in a multimaterial cell are implicitly defined by the level-set function and can be calculated by geometrical reconstruction.…”

“…The computational domain is discretized with a uniform Cartesian grid with constant cell spacing in axial and radial directions. The governing equations are solved on the numerical grid using our recently developed conservative, compressible multimaterial method [21]. This numerical approach allows us to consider multiple immiscible materials that are separated by a sharp interface.…”

“…where the three terms denote viscous, inertial, and surface-tension force effects. We employ the reduced interaction model [21] to simplify the computation of the interactions. In complex multiplematerial cells, only the two dominant, i.e., heaviest, phases are considered.…”

“…Moreover, the effects of another cellular-material layer in a compound cell model [20] and of bubble-bubble interactions are investigated. As experimental access even for laboratory generic configurations cannot provide fully detailed information on wave dynamics and hydrodynamic fields, we employ a state-of-the-art high-resolution numerical method for conservative multimaterial interface interaction [21].…”