Modified fractional-step methods for the Navier-Stokes equations

Exact Fractional Step Methods for Solving the Incompressible Navier-Stokes Equations

Fractional step (or projection) methods are a widely used technique for uncoupling the pressure solution in the incompressible Navier-Stokes equations while still satisfying the incompressibility constraint. Traditional fractional step methods have a time splitting error that can become quite significant if any of the terms in the momentum equation are treated implicitly. Higher order splitting...

Algebraic fractional-step schemes with spectral methods for the incompressible Navier-Stokes equations

The numerical investigation of a recent family of algebraic fractional-step methods for the solution of the incompressible time-dependent Navier–Stokes equations is presented. These methods are improved versions of the Yosida method proposed in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier–Stokes equations Comput. Methods Appl. Mech. En...

Numerical Methods for the Navier-Stokes equations

A Posteriori Error Estimation for the Fractional Step Theta Discretization of the Incompressible Navier-Stokes Equations

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time discretization. As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method. In every sub-step, the full incompressible system has to be solved (in contrast to time integrators of operator splitting type). The resulti...

A fractional step method for solving the compressible Navier-Stokes equations

This paper proposes a fractional step method for the calculation of compressible Navier–Stokes equations. The purpose of this study is to develop a robust and efficient numerical method for the simulation of low Mach number flows in which the poorly distributed eigenvalues usually result in the numerical difficulties. The method takes advantage of the pressurebased and the density-based methods...