Spectral discretization of the time‐dependent vorticity–velocity–pressure formulation of the Stokes problem

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

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 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 Vorticity-velocity-pressure formulation for Stokes problem

2003 ◽  
Vol 73 (248) ◽  
pp. 1673-1698 ◽  
Author(s):  
M. Amara ◽  
E. Chacón Vera ◽  
D. Trujillo
Keyword(s):  
Stokes Problem ◽  
Pressure Formulation ◽  
Velocity Pressure
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