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<!--- Don't mess with this line! --->{{Unreviewed|date=November 2013}}
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'''Solution algorithms for pressure-velocity coupling in [[steady flow]]s''' are the standard prepossessing methods used to solve steady flow problems in [[computational fluid dynamics]].
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The [[convection]] of the scalar variable Φ used to define fluid flow depends on the magnitude and direction of the local velocity field. In general, however the velocity field is not known. These algorithms are hence employed to obtain the solution.
 
The standard [[momentum and continuity equations]] can be given by:
 
'''The [[momentum equations]]'''
 
Obtained by substituting Φ with standard directional vectors of the velocity field ''u'', ''v'', and ''w''.
 
: <math>\frac{\partial  \rho uu }{\partial x} + \frac{\partial  \rho vu }{\partial y} = \frac{\partial \frac{ \nu \partial u} { \partial x}}{\partial x} + \frac{\partial \frac{ \nu \partial u} { \partial y}}{\partial y} - \frac{\partial p}{\partial x} + S_u  </math>
 
: <math>\frac{\partial  \rho uv }{\partial x} + \frac{\partial  \rho vv }{\partial y} = \frac{\partial \frac{ \nu \partial v} { \partial x}}{\partial x} + \frac{\partial \frac{ \nu \partial v} { \partial y}}{\partial y} - \frac{\partial p}{\partial y} + S_v  </math>
 
''' The [[continuity equation]] '''
 
: <math>\frac{\partial  \rho u }{\partial x} + \frac{\partial  \rho v }{\partial y} = 0 </math>
 
where <math>\rho</math> is the density, ''u'', ''v'', are the ''x''- and ''y''-directional components of velocity, ''p'' is the pressure field and ''S''<sub>''u'',''v''</sub> are the source terms.
 
These equations are however hard to solve due to non-linearity in the momentum equations and interdependence of the pressure term in all three equations. Also, for a general purpose flow equation, the pressure field is also unknown and is to be solved for as well.
 
If the flow field is compressible, the above equations act as the standard temperature and density equations and pressure can be found as it is a function of them both.
If, however the flow is in-compressible, the pressure is independent of density. Hence, coupling is necessary to induce a constraint on the solution. The resulting fields will then satisfy the continuity equations.
Both these issues are solved via the application of the SIMPLE Algorithm and its derivatives.
 
For general purpose and definition of these algorithms, a Staggered [[CFD Grid]] shall be used. It ensures the presence of very real non-zero pressure gradient across the nodes in any condition, even in the case of a checkered grid. The staggering also ensures realistic behaviors of the descretized momentum equations for spatially oscillating  pressures.
Also, the direction of the velocity vectors are exact.
 
== The staggered grid ==
 
[[File:Standard Staggered Grid in Computational Fluid Dynamics.jpg|Standard staggered grid in computational fluid dynamics]]
 
The above shows a standard grid used to solve staggered applications. The east, west, north and south notations are used. They direct the vector fields. The u component of velocity is stored in the e and w directions and the v component in the n and s directions. If 3-D fields are to applied, t and b can be used. These are basically vector control volumes different from the scalar pressure control volumes and different from each other.
 
The pressure gradient equations take a different form:
 
: <math> \frac {\partial p}{\partial x} = \frac{ P_p - P_w} { \partial x_u} </math> in the ''x''-direction
 
: <math> \frac {\partial p}{\partial y} = \frac{ P_p - P_s} { \partial y_v} </math> in the ''y''-direction
 
Furthermore, the momentum equations now take the form:
 
: <math>a_i,_J u_i,_J = \sum a_nb u_nb - \Delta V_u \frac {P_I,_J - P_{I-1},_J}{\partial x_u} + S \Delta V_u </math>
 
The summation covers all nodes and volumes in the immediate vicinity of the selected node. Their values are shown in the next figure.
 
[[File:Refined segregated Grid.jpg|Refined segregated Grid]]
 
Following this, The algorithms can be applied to get the solutions for the basic staggered grid equations.  
 
== SIMPLE algorithm ==
 
The acronym stands for Semi- Implicit method for pressure-linked equations. It is essentially a guess and correct procedure for the calculation of the staggered grid pressure field. These have been illustrated using a two dimensional steady flow.
[[File:Flow chart for SIMPLE Algorithm.jpg|thumb|Flow chart for SIMPLE Algorithm]]
'''Step 1 ''':- A pressure field p* is guessed.
 
'''Step 2 ''':- The Discretized momentum equations are solved using the value of p* to get velocity components u* and v*.
 
'''Step 3''':- Define the correction pressure as p' such that ''' p = p* + p' '''
 
'''Step 4''':- Similarly define the correction values for the velocities as u' and v' such that '''u = u* + u' ''' and '''v = v*+ v' '''
 
'''Step 5''':- Substitute the correct pressure field p in the momentum equations to obtain the correct velocity field (''u'',''v'').
 
'''Step 6 ''':- Subtract equations obtained in step 5 from those in step 1. We should get the equations in term of the correction terms (''u&prime;'' and ''v&prime;'')
 
'''Here we apply an assumption that <math> \sum a_{nb} u'_{nb} </math> and <math> \sum a_{nb} v'_{nb} </math> are 0 '''. This is the major assumption in the SIMPLE Algorithm.
This should then allow us to obtain the correction terms u' and v' of the Momentum Equations.
 
We can similarly find the correction terms for all nodes.
 
'''Step 7 ''':- Solve the continuity equation for the entire control volume. i.e. n,s,e,w nodes surrounding each node of the staggered grid, using the density terms.
 
'''Step 8 ''':- Substitute the corrected velocity equations in the continuity equations and separate the term containing the correction pressure p'.
 
This represents the equation for pressure correction p'.
 
'''Step 9 ''':- Solve the thus obtained equation to get the correction term and get the correct pressure. Use the new correct pressure to reiterate the entire process till a convergence is obtained.
 
''' Sometimes, the solution might not converge due to a large difference in the guessed field and correct pressure field. The new p= p* + αp'. α is kept between 0 and 1 to ensure convergence.'''
 
The choice of α decides the cost effectiveness of the solution.
 
== SIMPLER algorithm ==
 
[[File:Flow chart for the SIMPLER Algorithm.jpg|thumb|Flow chart for the SIMPLER Algorithm]]
The acronym for SIMPLE Revised, this algorithm is an improved version of the SIMPLE algorithm. Here the Discretised continuity equation is used to derive the correct intermediate pressure field instead of the correction pressure.
Refer to flow chart.
 
==SIMPLEC algorithm==
 
The SIMPLE Consistent Algorithm is almost same as the SIMPLE Algorithm, except that the manipulations are changed to ensure lesser omissions.
 
==References==
{{reflist}}
 
* ''Introduction to Computational Fluid Dynamics'' by Versteeg
* Patankar and Spalding, ''SIMPLE Algorithm'', 1972
* Patankar, ''SIMPLER Algorithm'', 1980
* Vandoormal and Raithby, ''SIMPLEC Algorithm'', 1984
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[[Category:Concepts in physics]]
[[Category:Equations of fluid dynamics]]
[[Category:Aerodynamics]]
[[Category:Partial differential equations]]
[[Category:Conservation equations]]
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Latest revision as of 22:13, 29 March 2014

If you'd like a property agent in Singapore to help you in your search for Singapore real estate or to promote or lease out your property in Singapore, without being pushed or pestered into making a choice you are not a hundred% comfortable with, perhaps I will help.

Once one has executed some analysis, that is, compiled a shortlist of criteria that they'd like their future dwelling to fulfill, expats can cross this list to their property agent. The agent will use this to assemble various available addresses that match all their listed points. The screening process that follows involves the agent taking expats on viewings in order that they'll acquaint themselves in individual with the kinds of houses that are accessible. As a result of they cope with property buyers, sellers, landlords and tenants, and since the transactions they deal with can contain massive sums of money, the necessity for professionalism is of utmost significance. Foreign Member of the Chartered Institute of Patent Brokers in the UK My Featured Properties of the Day! Click on it! View it!

Region Property Consultancy & Administration Providers Pte Ltd Citiprop Property Management Pte Ltd Knight Frank Property Community KF Property Network Pte Ltd Yong An Park (D09) – Condominium For Lease The Glyndebourne (D11) – Condominium For Rent Scotts 28 (D09) – Condominium For Rent Condominium For Lease – The Balmoral (D10) Beautiful apartment in the east, near MRT Casa Merah (D16) – Condominium For Hire Very spacious house near worldwide school Residence For Rent – Leonie Towers (D09) GETTING YOUR PROPERTY SOLD / LEASED? My point? Based on my expertise and what I have noticed, investing in property is the most typical manner for the common individual to construct up a significant amount of wealth However is not it dangerous to spend money on property now? Property Rotating Banner with Effects

Sure, shopping for a property will be risky, and the easiest way to manage that danger is to be prudent when you're shopping for, to do correct research on what you purchase, and to study as a lot as you may about property investing. Discovering your ultimate funding property Must do" property buying due diligence Two key tendencies that can drive the property market How interest rates affect property condo prices in singapore My cause for bringing this up is to pre warn others about leasing / renting in Singapore. We had no proof that the injury was not performed by us, we felt we have been badly treated over the entire issue. Timing for shifting in the new home and transferring out of your sold property Function the Property in the monthly publication of exclusive properties. Property and amenities management consultancy Brandon See

This is one other simple approach that many people normally do. If you don't have proper knowledge and skills concerning the PIC scheme, it is best to contact the IRAS division instantly. You'll be able to contact this department by way of email or phone without any hassles. The IRAS has some professional representatives who know methods to help all shoppers apply for the PIC grant easily. If you're a property agent, you must be capable of declare for this PIC scheme shortly with out having any issues.

The Letter of Intent accommodates quite a few important issues, such as a clause to protect you in the event your job unexpectedly terminates, you're moved to a different nation by your employer, or some other purpose it's a must to go away earlier than anticipated, thus permitting you to end your tenancy early if required. Nevertheless, that is only normally allowed in case your settlement is for a minimum of one yr. Even so, you'll usually nonetheless have to present at the least two months notice and with this clause in place, your landlord will have to refund your deposit.

Finding a Singapore property agent shouldn't be as difficult as it was before as now you can search for property brokers on-line. As there was an enormous increase in the number of internet customers, the real estate agents have additionally developed web sites for their agencies. You will get all the information about Singapore property agent by merely looking the web. There are also some boards that discusses about actual property brokers in Singapore and you can take a look at these forums for more data. The web Singapore property agent will aid you all the best way.

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