GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Solution of the Riemann problem of classical gasdynamics
Journal of Computational Physics
A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
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.