Finite-element preconditioning for pseudospectral solutions of elliptic problems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
An analysis of the fractional step method
Journal of Computational Physics
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Algebraic splitting for incompressible Navier-Stokes equations
Journal of Computational Physics
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A fast preconditioner for the incompressible Navier Stokes Equations
Computing and Visualization in Science
Pressure Correction Algebraic Splitting Methods for the Incompressible Navier-Stokes Equations
SIAM Journal on Numerical Analysis
Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier---Stokes Equations
Journal of Scientific Computing
ALADINS: An ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.45 |
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. Engrg. 188(1-3) (2000) 505-526; A. Quarteroni, F. Saleri, A. Veneziani, J. Math. Pures Appl. (9), 78(5) (1999) 473-503] and one of them (the Yosida4 method) is proposed in this paper for the first time. They rely on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the Navier-Stokes system, yielding a splitting in the velocity and pressure computation. In this paper, we analyze the numerical performances of these schemes when the space discretization is carried out with a spectral element method, with the aim of investigating the impact of the splitting on the global accuracy of the computation.