scholarly journals Existence of a martingale solution of the stochastic Navier–Stokes equations in unbounded 2D and 3D domains

2013 ◽  
Vol 254 (4) ◽  
pp. 1627-1685 ◽  
Author(s):  
Zdzisław Brzeźniak ◽  
Elżbieta Motyl
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Martingale Solution ◽  
2D And 3D

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Shock Wave Instability in a Channel with an Expansion Corner

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019 ◽  
Author(s):  
A. Kuzmin
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Variable Cross Section ◽  
Navier Stokes ◽  
Variable Cross ◽  
Navier Stokes Equations ◽  
Shock Position ◽  
Sonic Surface ◽  
2D And 3D ◽  
Subsonic Region

2D and 3D transonic flows in a channel of variable cross-section are studied numerically using a solver based on the Reynolds-averaged Navier–Stokes equations. The flow velocity is supersonic at the inlet and outlet of the channel. Between the supersonic regions, there is a local subsonic region whose upstream boundary is a shock wave, whereas the downstream boundary is a sonic surface. The sonic surface gives rise to an instability of the shock wave position in the channel. Computations reveal a hysteresis in the shock position versus the inflow Mach number. A dependence of the hysteresis on the velocity profile given at the inlet is examined.

scholarly journals Navier-Stokes Equations with Potentials

2007 ◽  
Vol 2007 ◽  
pp. 1-30 ◽  
Author(s):  
Adriana-Ioana Lefter
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Maximal Monotone Operator ◽  
Stokes Equations ◽  
Maximal Monotone ◽  
Existence Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nonlinear Semigroups ◽  
2D And 3D

We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.

MOTION OF GAS BUBBLES, CONSIDERED AS MASSLESS BODIES, AFFORDING DEFORMATIONS WITHIN A PRESCRIBED FAMILY OF SHAPES, IN AN INCOMPRESSIBLE FLUID UNDER THE ACTION OF GRAVITATION AND SURFACE TENSION

2007 ◽  
Vol 17 (09) ◽  
pp. 1445-1478
Author(s):  
ALEXEI LOZINSKI ◽  
MICHEL V. ROMERIO
Keyword(s):  
Surface Tension ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Gas Bubbles ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Navier Stokes Equations ◽  
D’Alembert Principle ◽  
Lagrangian Form ◽  
2D And 3D

A model allowing to describe motion and coalescence of gas bubbles in a liquid under the action of gravitation and surface tension is proposed. The shape of the bubbles is described by a pre-defined family of mappings, for example ellipsoids with a fixed volume and the effects of the gas motions inside the bubbles are neglected. The motion of a bubble is obtained in a Lagrangian form using the D'Alembert principle of virtual works. The set of equations is numerically solved with the help of the fictitious domain technique in which the Navier–Stokes equations in the domain formed by both fluid and gas are considered. The equations governing the bubbles motion are imposed by introducing Lagrange multipliers on the bubbles boundaries. Numerical results in 2D and 3D are presented.

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