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'''Vorticity confinement (VC)''', a physics-based [[computational fluid dynamics]] model analogous to [[shock capturing methods]], was invented by Dr. [[John Steinhoff]], professor at the University of Tennessee Space Institute, in the late 1980s | |||
<ref>{{Cite book | |||
| author=John Steinhoff | |||
| chapter=Vorticity Confinement: A New Technique for Computing Vortex Dominated Flows | |||
| title=Frontiers of Computational Fluid Dynamics | |||
| year=1994 | |||
| publisher=John Wiley & Sons | ISBN=0-471-95334-2 | |||
| url=http://www.alibris.com/search/books/isbn/9780471953340 | |||
}}</ref> | |||
to solve [[vortex]] dominated flows. | |||
It was first formulated to capture concentrated vortices shed from the wings, and later became popular in a wide range of research areas.<ref>{{Citation | |||
| last=Grossman | first=Bernard | last2=Hu | first2=Guangchu | |||
| title=The computation of massively separated flows using compressible vorticity confinement methods | |||
| journal=Computers and fluids | volume=35 | |||
| issue =7 | year=2006 | pages=781–789 | |||
| url=http://cat.inist.fr/?aModele=afficheN&cpsidt=17795373 | |||
}}.</ref> During the 1990s and 2000s, it became widely used in the field of engineering.<ref>{{Citation | |||
| last=Wenren | first=Y. | last2=Fan | first2=M. | |||
| last3=Dietz | first3=W. | last4=Hu | first4=G. | |||
| last5=Braun | first5=C. | last6=Steinhoff | first6=J. | |||
| last7=Grossman | first7=B. | |||
| title=Efficient Eulerian Computation of Realistic Rotorcraft Flows Using Vorticity Confinement | |||
| journal=AIAA | year=2001-0996 | |||
| url=http://www.flowanalysis.com/techinfo/aiaa-2001-0996.pdf | |||
}}.</ref><ref>{{Citation | |||
| last=Murayama | first=M. | last2=Nakahashi | first2=K. | |||
| last3=Obayashi | first3=S. | last4=Kato | first4=T. | |||
| title=Numerical Simulation of Vortical Flows Using Vorticity Confinement Coupled with Unstructured Adaptive Grid Refinement | |||
| journal=Computational Fluid Dynamics JOURNAL | |||
| volume=10 | issue=1 | pages=28–36 | |||
| year=2001 | |||
| url=http://www.ad.mech.tohoku.ac.jp/murayama/Papers/AIAA2001-0606.pdf | |||
}}.</ref> | |||
==The method== | |||
VC has a basic familiarity to [[soliton|solitary wave]] approach which is extensively used in many [[condensed matter physics]] applications.<ref>{{Citation | |||
| last=Bishop | first=A.R. | last2=Krumhansl | first2=J.A. | |||
| last3=Trullinger | first3=S.E. | |||
| title=Solitons in Condensed Matter: A Paradigm | |||
| journal=Physica D: Nonlinear Phenomena | |||
| volume=1 | issue =1 | year=1980 | pages=1–44 | |||
| url=http://adsabs.harvard.edu/abs/1980PhyD....1....1B | |||
| bibcode=1980PhyD....1....1B | doi=10.1016/0167-2789(80)90003-2 | |||
}}.</ref> The effect of VC is to capture the small scale features over as few as 2 grid cells as they convect through the flow. The basic idea is similar to that of compression [[discontinuity (mathematics)|discontinuity]] in Eulerian [[shock capturing methods]]. The internal structure is maintained thin and so the details of the internal structure may not be important. | |||
==Example== | |||
<!-- Deleted image removed: [[File:rotor flow.jpeg|thumb|right|Simulation of vortex sheets shed from helicopter rotor blades. {{Deletable image-caption|date=May 2012}}]] -->Consider 2D [[Euler equations]], modified using the confinement term, F: | |||
:<math> | |||
\frac{\partial \bold u}{\partial t} + \bold u \cdot \nabla \bold u + \nabla\frac{P}{\rho}=F_D (\bold u) -F_C (\bold u) | |||
</math> | |||
The discretized Euler equations with the extra term can be solved on fairly coarse grids, with simple low order accurate numerical methods, but still yield concentrated vortices which convect without spreading. VC has different forms, one of which is VC1. It involves an added dissipation,<math> F_D </math>,to the [[partial differential equation]], which when balanced with inward convection, <math> F_C </math>, produce stable solutions. Another form is termed as VC2 in which [[dissipation]] is balanced with nonlinear anti-diffusion to produce stable [[soliton|solitary wave]]-like solutions. | |||
:<math> | |||
F_D </math> : Dissipation | |||
:<math> | |||
F_C</math> : Inward convection for VC1 and nonlinear anti-diffusion for VC2 | |||
The main difference between VC1 and VC2 is that in the latter the centroid of the [[vortex]] follows the local velocity [[moment (physics)|moment]] weighted by vorticity. This should provide greater accuracy than VC1 in cases where the convecting field is weak compared to the self-induced [[velocity]] of the vortex. One drawback is that VC2 is not as robust as VC1 because while VC1 involves convection like inward propagation of vorticity balanced by an outward second order diffusion, VC2 involves a second order inward propagation of [[vorticity]] balanced by 4th order outward [[dissipation]]. This approach has been further extended to solve [[wave equation]] and is called [[Wave confinement]] (WC). | |||
==Immersed boundary== | |||
<!-- Deleted image removed: [[File:with VC.jpeg|thumb|right|Simulation of Jet plume with VC. {{Deletable image-caption|date=May 2012}}]] --><!-- Deleted image removed: [[File:without VC.jpeg|thumb|right|Simulation of Jet plume without VC. {{Deletable image-caption|date=May 2012}}]] -->To enforce no-slip boundary conditions on immersed surfaces, first, the surface is represented implicitly by a smooth “level set” function, “f”, defined at each grid point. This is the (signed) distance from each grid point to the nearest point on the surface of an object – positive outside, negative inside. Then, at each time step during the solution, velocities in the interior are set to zero. In a computation using VC, this results in a thin vortical region along the surface, which is smooth in the tangential direction, with no “staircase” effects.<ref>{{Citation | |||
| last=Wenren | first=Y. | last2=Fan | first2=M. | last5=Steinhoff | |||
| last3=Wang | first3=J. | last4=Xiao | first4=M. | |||
| title=Application of Vorticity Confinement to Prediction of the Flow over Complex Bodies | |||
| journal=AIAA Journal | |||
| volume=41 | issue=5 | year=2003 | pages=809–816 | |||
| url=http://adsabs.harvard.edu/abs/2003AIAAJ..41..809W | |||
| bibcode=2003AIAAJ..41..809W |doi= 10.2514/2.2042 | |||
}}.</ref> The important point is that no special logic is required in the “cut” cells, unlike many conventional schemes: only the same VC equations are applied, as in the rest of the grid, but with a different form for F. Also, unlike many conventional immersed surface schemes, which are inviscid because of cell size constraints, there is effectively a no-slip boundary condition, which results in a boundary layer with well-defined total vorticity and which, because of VC, remains thin, even after separation. The method is especially effective for complex configurations with separation from sharp corners. Also, even with constant coefficients, it can approximately treat separation from smooth surfaces. General blunt bodies, which typically shed turbulent vorticity that induces a velocity around an upstream body. It is inconsistent to use body fitted grids as the vorticity convects through a non fitted grid. | |||
==Applications== | |||
VC is used in many applications including rotor wake computations, computation of wing tip vortices, drag computations for vehicles, flow around urban layouts, smoke/contaminant propagation and special effects. Also, it is used in wave computations for communication purposes. | |||
==References== | |||
{{reflist}} | |||
{{Numerical PDE}} | |||
[[Category:Numerical differential equations]] | |||
[[Category:Computational fluid dynamics]] |
Revision as of 18:44, 12 December 2013
Vorticity confinement (VC), a physics-based computational fluid dynamics model analogous to shock capturing methods, was invented by Dr. John Steinhoff, professor at the University of Tennessee Space Institute, in the late 1980s [1] to solve vortex dominated flows. It was first formulated to capture concentrated vortices shed from the wings, and later became popular in a wide range of research areas.[2] During the 1990s and 2000s, it became widely used in the field of engineering.[3][4]
The method
VC has a basic familiarity to solitary wave approach which is extensively used in many condensed matter physics applications.[5] The effect of VC is to capture the small scale features over as few as 2 grid cells as they convect through the flow. The basic idea is similar to that of compression discontinuity in Eulerian shock capturing methods. The internal structure is maintained thin and so the details of the internal structure may not be important.
Example
Consider 2D Euler equations, modified using the confinement term, F:
The discretized Euler equations with the extra term can be solved on fairly coarse grids, with simple low order accurate numerical methods, but still yield concentrated vortices which convect without spreading. VC has different forms, one of which is VC1. It involves an added dissipation,,to the partial differential equation, which when balanced with inward convection, , produce stable solutions. Another form is termed as VC2 in which dissipation is balanced with nonlinear anti-diffusion to produce stable solitary wave-like solutions.
The main difference between VC1 and VC2 is that in the latter the centroid of the vortex follows the local velocity moment weighted by vorticity. This should provide greater accuracy than VC1 in cases where the convecting field is weak compared to the self-induced velocity of the vortex. One drawback is that VC2 is not as robust as VC1 because while VC1 involves convection like inward propagation of vorticity balanced by an outward second order diffusion, VC2 involves a second order inward propagation of vorticity balanced by 4th order outward dissipation. This approach has been further extended to solve wave equation and is called Wave confinement (WC).
Immersed boundary
To enforce no-slip boundary conditions on immersed surfaces, first, the surface is represented implicitly by a smooth “level set” function, “f”, defined at each grid point. This is the (signed) distance from each grid point to the nearest point on the surface of an object – positive outside, negative inside. Then, at each time step during the solution, velocities in the interior are set to zero. In a computation using VC, this results in a thin vortical region along the surface, which is smooth in the tangential direction, with no “staircase” effects.[6] The important point is that no special logic is required in the “cut” cells, unlike many conventional schemes: only the same VC equations are applied, as in the rest of the grid, but with a different form for F. Also, unlike many conventional immersed surface schemes, which are inviscid because of cell size constraints, there is effectively a no-slip boundary condition, which results in a boundary layer with well-defined total vorticity and which, because of VC, remains thin, even after separation. The method is especially effective for complex configurations with separation from sharp corners. Also, even with constant coefficients, it can approximately treat separation from smooth surfaces. General blunt bodies, which typically shed turbulent vorticity that induces a velocity around an upstream body. It is inconsistent to use body fitted grids as the vorticity convects through a non fitted grid.
Applications
VC is used in many applications including rotor wake computations, computation of wing tip vortices, drag computations for vehicles, flow around urban layouts, smoke/contaminant propagation and special effects. Also, it is used in wave computations for communication purposes.
References
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To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.