**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5

# Navier-Stokes equations Related Publications

##### 5 Mathematical Properties of the Viscous Rotating Stratified Fluid Counting with Salinity and Heat Transfer in a Layer

**Authors:**
A. Giniatoulline

**Abstract:**

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

**Keywords:**
Navier-Stokes equations,
Fourier transform,
stratified fluid,
generalized solutions

##### 4 On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid

**Authors:**
A. Giniatoulline

**Abstract:**

**Keywords:**
Navier-Stokes equations,
Galerkin Method,
nonlinear partial differential equations,
Sobolev spaces,
stratified fluid

##### 3 Comparison of Two Types of Preconditioners for Stokes and Linearized Navier-Stokes Equations

**Authors:**
Ze-Jun Hu,
Ting-Zhu Huang,
Ning-Bo Tan

**Abstract:**

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package.

**Keywords:**
Navier-Stokes equations,
Krylov subspace method,
preconditioner,
dimensional splitting,
augmented Lagrangian preconditioner

##### 2 Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates

**Authors:**
Rana Khalid Naeem,
Asif Mansoor,
Waseem Ahmed Khan,
Aurangzaib

**Abstract:**

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating that the flow equations possess an infinite set of solutions.

**Keywords:**
Navier-Stokes equations,
exact solutions,
Fluid of variable viscosity,
Steady plane flows

##### 1 Toward a New Simple Analytical Formulation of Navier-Stokes Equations

**Authors:**
Gunawan Nugroho,
Ahmed M. S. Ali,
Zainal A. Abdul Karim

**Abstract:**

**Keywords:**
Turbulent flows,
Navier-Stokes equations,
potential function