A note on Milne-Thomson's general solution of Navier–Stokes equations

1965 ◽  
Vol 61 (4) ◽  
pp. 915-916
Author(s):  
G. D. Nigam
Keyword(s):  
General Solution ◽  
Force Field ◽  
Velocity Vector ◽  
Stokes Equations ◽  
Scalar Potential ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
External Force Field ◽  
Image Position

The Navier–Stokes equations governing the motion of viscous compressible fluids arewhere ρ is the density, q is the velocity vector, V is the scalar potential of the external force field, I is the idemfactor and Φ is the stress-tensorMilne-Thomson ((l)) has given a general solution of (1) and (2) in the form

scholarly journals Detection of multiple solutions using a mid-cell back substitution technique applied to computational fluid dynamics

2000 ◽  
Vol 214 (11) ◽  
pp. 1401-1407
Author(s):  
S R Kendall ◽  
H V Rao
Keyword(s):  
Multiple Solutions ◽  
Computational Models ◽  
Stokes Equations ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Algebraic Equations ◽  
Navier Stokes Equations ◽  
Flow Modelling ◽  
Spurious Solutions ◽  
Linear Algebraic Equations

Computational models for fluid flow based on the Navier-Stokes equations for compressible fluids led to numerical procedures requiring the solution of simultaneous non-linear algebraic equations. These give rise to the possibility of multiple solutions, and hence there is a need to monitor convergence towards a physically meaningful flow field. The number of possible solutions that may arise is examined, and a mid-cell back substitution technique (MCBST) is developed to detect and avoid convergence towards apparently spurious solutions. The MCBST was used successfully for flow modelling in micron-sized flow passages, and was found to be particularly useful in the early stages of computation, optimizing the speed of convergence.

scholarly journals About general solutions of Euler’s and Navier-Stokes equations

2019 ◽  
pp. 190-193
Author(s):  
V. I. Rozumniuk
Keyword(s):  
General Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Fundamental Problem ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
General Solutions ◽  
And Diffusion

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

ANALYSIS OF A PHASE-FIELD MODEL FOR TWO-PHASE COMPRESSIBLE FLUIDS

2010 ◽  
Vol 20 (07) ◽  
pp. 1129-1160 ◽  
Author(s):  
EDUARD FEIREISL ◽  
HANA PETZELTOVÁ ◽  
ELISABETTA ROCCA ◽  
GIULIO SCHIMPERNA
Keyword(s):  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Immiscible Fluids ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Cahn Equation ◽  
System Coupling

A model describing the evolution of a binary mixture of compressible, viscous, and macroscopically immiscible fluids is investigated. The existence of global-in-time weak solutions for the resulting system coupling the compressible Navier–Stokes equations governing the motion of the mixture with the Allen–Cahn equation for the order parameter is proved without any restriction on the size of initial data.

Sign in / Sign up

Export Citation Format

Share Document