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.