Estimates of deviations from the exact solution of the Stokes problem in the vorticity-velocity-pressure formulation

2012 ◽  
Vol 185 (5) ◽  
pp. 698-706
Author(s):  
A. Mikhaylov ◽  
S. Repin
Keyword(s):  
Exact Solution ◽  
Stokes Problem ◽  
Pressure Formulation ◽  
Velocity Pressure

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

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.

Natural Steady Convection in a Space Annulus Between Two Elliptic Confocal Ducts: Influence of the Slope Angle

2005 ◽  
Vol 73 (1) ◽  
pp. 88-95 ◽  
Author(s):  
Mahfoud Djezzar ◽  
Michel Daguenet
Keyword(s):  
Slope Angle ◽  
Boussinesq Equations ◽  
Annular Space ◽  
Arbitrary Angle ◽  
Elliptic Coordinates ◽  
System A ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Steady Convection ◽  
Calculation Code

The authors express the Boussinesq equations of the laminar thermal and natural convection, in the case of permanent and bidimensional flow, in an annular space between two confocal elliptic cylinders. The latter is oriented at an arbitrary angle α with respect to the gravity force, using the elliptic coordinates system. A new calculation code using the finite volumes with the primitive functions (velocity-pressure formulation) is proposed. The Prandtl number is fixed at 0.7 (case of the air) with varying the Rayleigh number. The effect of the system inclination is examined.

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