one Dimensional Navier Stokes Code
 

Dear Friends,

I want to solve

du/dt+ u . du/dx = -dp/dx

Can someone direct me or provide me with a code for solving this equation ?

Thanks for your time

CFDtoy

Re: one Dimensional Navier Stokes Code
 

Well, CFDtoy, you haven't adequately defined the problem you'd like to solve. Here in the Yankees organization, we like to have the following pieces of information before solving a PDE.

1) Define the space. Where do you want to solve this equation? On the infinite line -inf < x < inf ? On the line segment 0 < x < L ?

2) Boundary conditions. Now that you know where (in x) that you're looking, you must specify what's going on at the boundary. Are you fixing the variable 'u' to be 0 at each boundary? Steinbrenner usually likes to assume periodic boundary conditions when he's just playing around, since there are some methods that thoroughly exploit this structure - so called Spectral Methods, which, as you may or may not be aware, are based on Fourier analysis. Actually, some historians point out that Joe Dimaggio may have independently discovered Fourier analysis while studying the wave-particle properties of the knuckleball.

3) What is 'p'? To close the problem, you must either provide an equation for 'p', or simply specify it (which, while simple, could be instructive depending on how much you already know).

There are literally hundreds of ways of numerically investigating this problem. Given a reasonably nice 'p', you can actually solve this exactly by hand with little trouble. Even for a nasty 'p', you can use the method of characteristics to solve the problem (but you're going to need to know about shocks if you solve by hand. Like when the Red Sox trade Babe Ruth to your team. That kind of shock.)

So complete the description of the problem, and stop by Yankees Stadium in the Bronx. Ask to speak to Derek Jeter - my office is on the 11th floor, magneto-hydrodynamics division, New York Yankees.

D. Jeter, Ph.D.

Re: one Dimensional Navier Stokes Code
 

Hello Jeter,

Thanks for the reply. Here are certain Flow Characteristics : Domain : 0<x<L say [0,1] p inlet =10 Kpa P out = 1 kpa Vel. inlet = 0.1 m/s Vel . Exit - Outflow

Can you help me with a Code say with some kind of Pressure Correction Algorithm such as SIMPLE .

Thanks

CFDtoy

Re: one Dimensional Navier Stokes Code
 

Hello Jeter,

Thanks for the reply. Here are certain Flow Characteristics :

Domain : 0<x<L say [0,1]

p inlet =10 Kpa

P out = 1 kpa

Vel. inlet = 0.1 m/s

Vel . Exit - Outflow

Can you help me with a Code say with some kind of Pressure Correction Algorithm such as SIMPLE .

Thanks

CFDtoy

Re: one Dimensional Navier Stokes Code
 

Hello Jeter,

Thanks for the reply. Here are certain Flow Characteristics :

domain extending through a distance starting from 0 to L

p inlet =10 Kpa

P out = 1 kpa

Vel. inlet = 0.1 m/s

Vel . Exit - Outflow

Can you help me with a Code say with some kind of Pressure Correction Algorithm such as SIMPLE .

Thanks

CFDtoy

Re: one Dimensional Navier Stokes Code
 

Is this for an incompressible flow? 1D incompressible flows are not very interesting, because the divergence free condition kills you instantly.

Re: one Dimensional Navier Stokes Code
 

Hi noName,

It is an incompressible Flow. why do you think the divergence free is not going to give a smooth ride? in fact most literature do talk about incompressible flow and simple divergence free condition.

Thanks for the help. If you come across any simple code that solves a incompressible flow eqn ( with viscosity) I request you to kindly help me with one.

I appreciate your time and help.

CFDtoy

Re: one Dimensional Navier Stokes Code
 

Simple:

In 1 dimension, the divergence-free condition is just du/dx=0, and therefore the velocity u is constant in x. This is boring!

Re: one Dimensional Navier Stokes Code
 

Hello

Very true ..but for a constant duct area.

if d(UA)/dx=0 and

du/dt+1/A*d(U*U*A)/dx=-dp/dx

A- area of cross section changing the problem has a nice solution at steady state.

now things shud start the discussion.

Thanks

CFDtoy

help
 

can u help me to write c program for solving1d heat equation in explicit form?