Generating inviscid and viscous fluid flow simulations over a surface using a quasi-simultaneous technique

1. A computer-implemented method of generating a fluid-flow simulation over a computer-generated surface using one or more processors, the simulation including an inviscid fluid-flow mesh comprised of a plurality of inviscid fluid cells and a viscous fluid-flow mesh comprised of a plurality of boundary-layer fluid cells, at least some of the boundary-layer fluid cells being on or adjacent to the computer-generated surface, the method comprising:

determining, using the one or more processors, an initial fluid property, for at least one inviscid fluid cell using an inviscid fluid simulation that does not simulate fluid viscous effects;

determining, using the one or more processors, an initial boundary-layer fluid property for at least one of the boundary-layer fluid cells using the initial fluid property and a viscous fluid simulation that simulates fluid viscous effects,

wherein the at least one inviscid fluid cell is located in relation to the at least one boundary-layer fluid cell such that an updated boundary-layer fluid property for the at least one boundary-layer fluid cell is influenced by the at least one inviscid fluid cell;

determining, using the one or more processors, the updated boundary-layer fluid property for the at least one boundary-layer fluid cell using the initial fluid property, initial boundary-layer fluid property, and an interaction law,

wherein the interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using a two-dimensional surface panel technique and a fluid-property vector;

determining, using the one or more processors, an updated fluid property for the at least one inviscid fluid cell using the updated boundary-layer fluid property.

2. The computer-implemented method of claim 1 , wherein the initial fluid property is an initial fluid velocity and the updated fluid property is an updated fluid velocity.

3. The computer-implemented method of claim 1 , wherein the initial boundary-layer fluid property is an initial displacement thickness and the updated boundary-layer fluid property is an updated displacement thickness.

4. The computer-implemented method of claim 1 , wherein the matrix of aerodynamic influence coefficients is adapted to account for compressibility by dividing each row by (1−M 1 2 ) 1/2 , wherein M 1 is the local Mach number.

5. The computer-implemented method of claim 1 , wherein a fluid property of the fluid property vector is determined using the following relation to simulate supersonic flow conditions:

u

e

⁡

(

n

+

1

)

=

u

e

⁡

(

n

)

-

1

M

ei

2

-

1

⁢

(

ⅆ

m

(

n

)

ⅆ

s

-

ⅆ

m

(

n

+

1

)

ⅆ

s

)

,

where u e(n+1) is the edge velocity at time step n+1, u e(n) is the edge velocity at time step n, M ei is the local Mach number, and m (n) and m (n+1) is the product of: edge density ρ e , edge velocity u e , and boundary-layer thickness δ* at time step n and time step n+1, respectively.

6. The computer-implemented method of claim 1 , wherein a fluid property of the fluid property vector is determined using the following relation to simulate supersonic flow conditions over a swept/tapered wing:

u

e

⁡

(

n

+

1

)

=

u

e

⁡

(

n

)

-

1

M

ei

2

-

1

⁢

(

v

w

⁡

(

n

+

1

)

-

v

w

⁡

(

n

)

)

,

where u e(n+l) is the edge velocity at time step n+1, u e(n) is the edge velocity at time step n, M ei is the local Mach number, and v w(n+1) and v w(n) are the transpiration velocities at the surface at time step n and time step n+1, respectively.

7. The computer-implemented method of claim 1 , wherein the matrix of aerodynamic influence coefficients is adapted row-by-row to implement either the subsonic or supersonic interaction law depending on the local Mach number.

8. The computer-implemented method of claim 7 , wherein the matrix of aerodynamic influence coefficients is further adapted to utilize a linear weighted average of the subsonic and supersonic interaction laws to approximate the changes to the inviscid fluid flow for local Mach numbers near Mach 1.

9. The computer-implemented method of claim 8 , wherein the linear weighted average is used for local Mach numbers ranging between about 0.97 and about 1.03.

10. The computer-implemented method of claim 1 , wherein the matrix of aerodynamic influence coefficients is adapted using a curvature correction to approximate a boundary layer characterized as having a thickness and a curvature.

11. The computer-implemented method of claim 1 , wherein the interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using an axisymmetric surface panel technique instead of a two-dimensional surface panel technique.

12. The computer-implemented method of claim 1 , wherein the computer-generated surface is a computer-generated wing surface of an aircraft.

13. A non-transitory computer-readable storage medium comprising computer-executable instructions for generating a fluid-flow simulation over a computer-generated surface, the simulation including an inviscid fluid-flow mesh comprised of a plurality of inviscid fluid cells and a viscous fluid-flow mesh comprised of a plurality of boundary-layer fluid cells, at least some of the boundary-layer fluid cells being on or adjacent to the computer-generated surface, the instructions for:

determining an initial fluid property, for at least one inviscid fluid cell using an inviscid fluid simulation that does not simulate fluid viscous effects;

determining an initial boundary-layer fluid property for at least one of the boundary-layer fluid cells using the initial fluid property and a viscous fluid simulation that simulates fluid viscous effects,

wherein the at least one inviscid fluid cell is located in relation to the at least one boundary-layer fluid cell such that an updated boundary-layer fluid property for the at least one boundary-layer fluid cell is influenced by the at least one inviscid fluid cell;

determining the updated boundary-layer fluid property for the at least one boundary-layer fluid cell using the initial fluid property, initial boundary-layer fluid property, and an interaction law,

wherein the interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using a two-dimensional surface panel technique and a fluid-property vector;

determining an updated fluid property for the at least one inviscid fluid cell using the updated boundary-layer fluid property.

14. The computer-readable medium of claim 13 , wherein the initial fluid property is an initial fluid velocity and the updated fluid property is an updated fluid velocity.

15. The computer-readable medium of claim 13 , wherein the initial boundary-layer fluid property is an initial displacement thickness and the updated boundary-layer fluid property is an updated displacement thickness.

16. The computer-readable medium of claim 13 , wherein the matrix of aerodynamic influence coefficients is adapted to account for compressibility by dividing each row by (1−M 1 2 ) 1/2 , wherein M 1 is the local Mach number.

17. The computer-readable medium of claim 13 , wherein a fluid property of the fluid property vector is determined using the following relation to simulate supersonic flow conditions:

u

e

⁡

(

n

+

1

)

=

u

e

⁡

(

n

)

-

1

M

ei

2

-

1

⁢

(

ⅆ

m

(

n

)

ⅆ

s

-

ⅆ

m

(

n

+

1

)

ⅆ

s

)

,

where u e(n+1) is the edge velocity at time step n+1, u e(n) is the edge velocity at time step n, M ei is the local Mach number, and m (n) and m( n+1) is the product of: edge density ρ e , edge velocity u e , and boundary-layer thickness δ* at time step n and time step n+1, respectively.

18. The computer-readable medium of claim 13 , wherein a fluid property of the fluid property vector is determined using the following relation to simulate supersonic flow conditions over a swept/tapered wing:

u

e

⁡

(

n

+

1

)

=

u

e

⁡

(

n

)

-

1

M

ei

2

-

1

⁢

(

v

w

⁡

(

n

+

1

)

-

v

w

⁡

(

n

)

)

,

where u e(n+1) is the edge velocity at time step n+1, u e(n) is the edge velocity at time step n, M ei is the local Mach number, and v w(n+1) and v w(n) are the transpiration velocities at the surface at time step n and time step n+1, respectively.

19. The computer-readable medium of claim 13 , wherein the matrix of aerodynamic influence coefficients is adapted row-by-row to implement either the subsonic or supersonic interaction law depending on the local Mach number.

20. The computer-readable medium of claim 19 , wherein the matrix of aerodynamic influence coefficients is further adapted to utilize a linear weighted average of the subsonic and supersonic interaction laws to approximate the changes to the inviscid fluid flow for local Mach numbers near Mach 1.

21. The computer-readable medium of claim 20 , wherein the linear weighted average is used for local Mach numbers ranging between about 0.97 and about 1.03.

22. The computer-readable medium of claim 13 , wherein the matrix of aerodynamic influence coefficients is adapted using a curvature correction to approximate a boundary layer characterized as having a thickness and a curvature.

23. The computer-readable medium of claim 13 , wherein the interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using an axisymmetric surface panel technique instead of a two-dimensional surface panel technique.

24. The computer-readable medium of claim 13 , wherein the computer-generated surface is a computer-generated wing surface of an aircraft.