A linear, decoupled fractional time-stepping method for the nonlinear fluid-fluid interaction. (English) Zbl 1423.76253
Summary: In this paper, a linear decoupled fractional time stepping method is proposed and developed for the nonlinear fluid-fluid interaction governed by the two Navier-Stokes equations. Partitioned time stepping method is applied to two-physics problems with stiffness of the coupling terms being treated explicitly and is also unconditionally stable. As for each fluid, the velocity and pressure are respectively determined by just solving one vector-valued quasi-elliptic equation and the Possion equation with homogeneous Neumann boundary condition per time step. Therefore, the cost of the fluid-fluid interaction is dominant to solve four simple linear equations, which greatly reduces the computational cost of the whole system. The method exploits properties of the fluid-fluid system to establish its stability and convergence with the same results as the standard scheme. Finally, numerical experiments are presented to show the performance of the proposed method.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35R11 | Fractional partial differential equations |
| 76T99 | Multiphase and multicomponent flows |
Keywords:
convergence; fluid-fluid interface; fractional time-stepping method; Navier-Stokes equations; numerical experimentsReferences:
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