Universal Wall Boundary Condition Treatment for K-Omega Turbulence Models

1 . A computer-implemented method for simulating fluid flow about a simulated physical object, the method comprising:

receiving by one or more computing systems, a model of a simulation space that includes a mesh defining a representation of the physical object in the simulation space, with the mesh comprising plural cells having resolutions to account for surfaces of the physical object;

determining boundary conditions for a specific energy dissipation rate of a k-Omega turbulence fluid flow model of the simulated fluid flow, by:

computing by the one or more computing systems, a generalized wall-boundary condition from fluid flow variables, a value of the specific energy dissipation rate for a turbulent flow that is valid for a viscous layer, buffer layer, and logarithmic region of a boundary defined in the simulation space.

2 . The method of claim 1 wherein for a cell located at a position y+<3 of the boundary where y is a cell at the boundary, the method further comprises:

applying by the one or more computing systems, a buffer layer correction factor as a boundary condition for the energy dissipation rate.

3 . The method of claim 1 wherein determining the boundary conditions further comprises:

applying by the one or more computing systems, a buffer layer correction factor as a boundary condition for the energy dissipation rate for a cell located at a position y+<3 of the boundary where y is a cell at the boundary, and the correction factor is given according to:

ω′ Hyb =f blend ω Hyb

where ω′ Hyb is the correction factor f blend is a blending function and ω Hyb is a viscus layer correction function.

4 . The method of claim 1 , further comprises:

applying by the one or more computing systems, a viscous sublayer correction factor as a boundary condition for the energy dissipation rate.

5 . The method of claim 1 wherein determining the boundary conditions further comprises:

applying by the one or more computing systems, a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is a cell at location 1 and y 2 2 is the cell at position 2.

6 . The method of claim 3 wherein determining the boundary conditions further comprises:

applying by the one or more computing systems, a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is the cell at location 1 and y 2 2 is the cell at position 2.

7 . The method of claim 1 , further comprising:

accessing the k-Omega model;

initializing the accessed k-Omega model with the determined boundary conditions; and

executing the initialized k-Omega model to simulated the fluid flow about the simulated physical object.

8 . The method of claim 1 , further comprising:

accessing the k-Omega turbulence fluid flow model, with the k-Omega turbulence fluid flow model, including

a first partial differential equation to determine turbulent kinetic energy of the fluid flow; and

a second partial differential equation to determine the specific energy dissipation rate of the fluid flow in the simulation space.

9 . The method of claim 1 , further comprising:

determining whether the location is at a buffer layer; and when at the buffer layer,

applying a correction that increase the values of energy dissipation rate only at the buffer layer by:

applying a blending function that acts on the values of energy dissipation rate at the buffer layer and prevents the blending function to affect values at the viscous layer of the boundary defined in the simulation space.

10 . The method of claim 9 wherein applying the correction further comprises:

applying a blending function that acts on the values of energy dissipation rate at the buffer layer and prevents the blending function to affect values at the viscous layer of the boundary defined in the simulation space.

11 . A system for simulating a physical process flow about a simulated physical object, the system comprising:

one or more processor devices;

memory operatively coupled to the one or more processor devices;

storage media storing a computer program comprising instructions to cause the system to:

receive a model of a simulation space that includes a mesh defining a representation of the physical object in the simulation space, with the mesh comprising plural cells having resolutions to account for surfaces of the physical object;

determine boundary conditions for a specific energy dissipation rate of a k-Omega turbulence fluid flow model of the simulated fluid flow, by instructions to cause the system to:

compute from fluid flow variables a value of the specific energy dissipation rate for a turbulent flow that is valid for a viscous layer, buffer layer, and logarithmic region of a boundary defined in the simulation space.

12 . The system of claim 11 , further configured to:

determine that a cell is located at a position y+<3 of the boundary where y is a cell at the boundary; and

apply a buffer layer correction factor as a boundary condition for the energy dissipation rate, with the correction factor given according to:

ω′ Hyb =f blend ω Hyb

where ω′ Hyb is the correction factor f blend is a blending function and ω Hyb is a viscus layer correction function.

13 . The system of claim 11 , further configured to:

apply a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is a cell at location 1 and y 2 2 is the cell at position 2.

14 . The system of claim 12 , further configured to:

apply a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is the cell at location 1 and A is the cell at position 2.

15 . The system of claim 12 , further configured to:

access the k-Omega model;

initialize the accessed k-Omega model with the determined boundary conditions; and

execute the initialized k-Omega model to simulated the fluid flow about the simulated physical object.

16 . A computer program product for simulating a physical process,

the computer program product tangibly stored on a non-transitory computer readable storage medium, the computer program product comprising instructions to cause a system to:

receive a model of a simulation space that includes a mesh defining a representation of the physical object in the simulation space, with the mesh comprising plural cells having resolutions to account for surfaces of the physical object;

determine boundary conditions for a specific energy dissipation rate of a k-Omega turbulence fluid flow model of the simulated fluid flow, by instructions to cause the system to:

compute from fluid flow variables a value of the specific energy dissipation rate for a turbulent flow that is valid for a viscous layer, buffer layer, and logarithmic region of a boundary defined in the simulation space.

17 . The computer program product of claim 16 , further comprising instructions to cause the system to:

determine that a cell is located at a position y+<3 of the boundary where y is a cell at the boundary; and

apply a buffer layer correction factor as a boundary condition for the energy dissipation rate, with the correction factor given according to:

ω′ Hyb =f blend ω Hyb

where ω′ Hyb is the correction factor f blend is a blending function and ω Hyb is a viscus layer correction function.

18 . The computer program product of claim 16 , further comprising instructions to cause the system to:

apply a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is a cell at location 1 and y 2 2 is the cell at position 2.

19 . The computer program product of claim 18 , further comprising instructions to cause the system to:

apply a viscous sublayer correction factor as a boundary condition for the energy dissipation rate, with the viscous sublayer correction factor given according to:

∂

ω

v

f

∂

y

=

∂

ω

v

d

∂

y

⁢

⌊

y

1

2

⁢

y

2

2

(

y

2

+

y

1

2

)

4

⌋

where

∂

ω

v

f

∂

y

is the correction factor, y 1 2 is the cell at location 1 and y 2 2 is the cell at position 2.

20 . The computer program product of claim 16 , further comprising instructions to cause the system to:

access the k-Omega model;

initialize the accessed k-Omega model with the determined boundary conditions; and

execute the initialized k-Omega model to simulated the fluid flow about the simulated physical object.