... Navier–Stokes–Cahn–Hilliard ( NSCH ) equations is challenging due to spatiotemporal multiscale behavior, ε -conditional stability and ill-conditioning. The purpose of this work is to evaluate higher-order generalized-α time-integration methods, focusing on the third-order scheme...

... spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency. Originality/value The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous...

...-order system problems. Findings The proposed method is capable of coupling different spatial methods for multiple subdomains and different implicit/explicit time integration schemes in the GS4 framework while sustaining second-order time accuracy. Originality/value Traditional approaches do...

... integration process for solving the two phase flow dynamics with reactions. Findings Numerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second...

... applications to time dependent Burgers’ equation, which is well-known to serve as a simplified model of fluid dynamics, for illustrations of the essential concepts. Design/methodology/approach – The framework permits, for a very general family of time integrators where traditional methods are a subset...

...Masao Shimada; David Tae; Tao Xue; Rohit Deokar; K K Tamma Purpose – The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g...