Operator splitting for two-dimensional incompressible fluid equations
نویسندگان
چکیده
We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier–Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
منابع مشابه
Numerical Analysis and Scientific Computing Preprint Seria A modular, operator splitting scheme for fluid-structure interaction problems with thick structures
We present an operator-splitting scheme for fluid-structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier-Stokes equations for an incompressible viscous fluid are used to model the fluid. The operator splitting...
متن کاملStabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling
In this paper we present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/hp element methods applied to the solution of the incompressible Navier–Stokes equations. We construct the SVV around a filter with respect to an orthogonal expansions, and prove that this methodology provides a symmetric semi-positive definite SVV operator. After providing a few simpl...
متن کاملAn overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most compu...
متن کاملA Splitting Method Using Discontinuous Galerkin for the Transient Incompressible Navier-stokes Equations
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments. Mathematics Subject Classification. 65M12, 65M15, 65M60. Re...
متن کاملExistence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition
We study a nonlinear, moving boundary fluid-structure interaction (FSI) problem between an incompressible, viscous Newtonian fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The fluid and structure are coupled via the Navier slip boundary condition and balance of contact forces at the fluid-structure interface. The slip boundary...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 82 شماره
صفحات -
تاریخ انتشار 2013