scholarly journals Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2906
Author(s):  
Jaroslav Haslinger ◽  
Radek Kučera ◽  
Kristina Motyčková ◽  
Václav Šátek
Keyword(s):  
Stokes Flow ◽  
Interior Point Method ◽  
Mixed Finite Elements ◽  
Path Following ◽  
Preconditioned Conjugate Gradient ◽  
Active Set ◽  
Pressure Formulation ◽  
Three Space ◽  
Velocity Pressure ◽  
Inequality Type

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.

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.

scholarly journals Analysis and Approximation of a Vorticity–Velocity–Pressure Formulation for the Oseen Equations

2019 ◽  
Vol 80 (3) ◽  
pp. 1577-1606 ◽  
Author(s):  
V. Anaya ◽  
A. Bouharguane ◽  
D. Mora ◽  
C. Reales ◽  
R. Ruiz-Baier ◽  
...  
Keyword(s):  
Oseen Equations ◽  
Pressure Formulation ◽  
Velocity Pressure

scholarly journals Analytical solution for viscous incompressible Stokes flow in a spherical shell

Solid Earth ◽  
2017 ◽  
Vol 8 (6) ◽  
pp. 1181-1191 ◽  
Author(s):  
Cedric Thieulot
Keyword(s):  
Finite Element ◽  
Spherical Shell ◽  
Stokes Flow ◽  
Body Force ◽  
Convergence Rates ◽  
Mean Square ◽  
Root Mean Square Velocity ◽  
New Family ◽  
Incompressible Stokes Flow ◽  
Velocity Pressure

Abstract. I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial and of the power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g., the root mean square velocity, are analytically computed. This forms the basis of a numerical benchmark for convection codes and I have implemented it in two finite-element codes: ASPECT and ELEFANT. I report error convergence rates for velocity and pressure.

scholarly journals Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface-Piercing Cylinder

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Agostino Lauria ◽  
Leonardo Primavera
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
The Subject ◽  
Run Up ◽  
Velocity Pressure

Due to its relevance in ocean engineering, the subject of the flow field generated by water waves around a vertical circular cylinder piercing the free surface has recently started to be considered by several research groups. In particular, we studied this problem starting from the velocity-potential framework, then the implementation of the numerical solution of the Euler equations in their velocity-pressure formulation, and finally the performance of the integration of the Navier-Stokes equations in primitive variables. We also developed and applied methods of extraction of the flow coherent structures and most energetic modes. In this work, we present some new results of our research directed, in particular, toward the clarification of the main nonintuitive character of the phenomenon of interaction between a wave and a surface-piercing cylinder, namely, the fact that the wave exerts its maximum force and exhibits its maximum run-up on the cylindrical obstacle at different instants. The understanding of this phenomenon becomes of crucial importance in the perspective of governing the entity of the wave run-up on the obstacle by means of wave-flow-control techniques.

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