A second-order time-accurate implicit finite volume method with exact two-phase Riemann problems for compressible multi-phase fluid and fluid-structure problems

A family of compressible multi-phase fluid and fluid-structure interaction problems for which implicit schemes are preferable over explicit counterparts is identified. Using as a backdrop a finite volume method based on exact two-phase Riemann problems that has proven to be robust for multi-phase flows with strong contact discontinuities and highly nonlinear fluid-structure interaction problems, an implicit computational framework for the solution of such problems is presented. General issues that arise in the context of second- and higher-order time-discretizations of multi-material problems by multi-step schemes are highlighted, and solutions to these issues are presented in the form of redesigned implicit time-integrators. The proposed implicit computational framework is illustrated with the solution of an air-water shock tube problem, a realistic compressible multi-phase fluid problem, and a highly nonlinear fluid-structure interaction problem associated with the underwater implosion of a cylindrical shell. In all cases, the accuracy and robustness of the proposed implicit computational framework are demonstrated, and its superior computational performance is highlighted.