scholarly journals Enhanced algorithms for solving the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi ◽  
Henda Ouertani
Keyword(s):  
Stokes Problem ◽  
Navier Stokes ◽  
Uzawa Method ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

AbstractThe objective of the article is to improve the algorithms for the resolution of the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem in two and three domains. Two algorithms are proposed. The first one is based on the Uzawa method. In the second one we consider a modified global resolution. The two algorithms are implemented and their results are compared.

scholarly journals Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Time Discretization ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the variational formulation deduced from the nonstationary Navier–Stokes equations is discretized using the spectral method. We prove that the time semidiscrete problem and the full spectral discrete one admit at most one solution.

scholarly journals Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Ebtisam Alharbi ◽  
Nejmeddine Chorfi ◽  
Henda Ouertani
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Navier Stokes Equations ◽  
Implicit Euler Scheme ◽  
Numerical Tests ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced from the implicit Euler scheme in time and spectral methods in space. We present a matrix linear system and some numerical tests, which are in perfect concordance with the analysis.

Sign in / Sign up

Export Citation Format

Share Document