Coupling of STAR-CCM+ to Other

Theoretical or Numerical Solutions

Milovan Perić

• The need to couple STAR-CCM+ with other theoretical or

numerical solutions

• Coupling approaches: surface and volume coupling

• Examples of surface and volume coupling

• Future developments

Contents

• Eliminate reflections from boundaries (especially inlet)

• Reduce the size of 3D simulation domain (reduce

computing cost, especially for long-lasting transient

simulations)

• Enable simulation of wave propagation over long

distance (wake signature, shore impact etc.)

Need for Coupling

Source: Wikipedia

• An example of surface coupling is Fluid-Structure-

Interaction (FSI): the solutions in fluid and structure are

coupled at the contact surface…

• The same approach can be applied to two fluid domains,

whereas in each domain different equations (potential

flow, Euler- or Navier-Stokes equations) can be solved

with different methods (boundary element, finite element

or finite volume).

• There are many different options (implicit or explicit

coupling, solving simultaneously for the whole domain or

using solution in one subdomain to impose boundary

conditions in another subdomain, one- or two-way…).

Surface Coupling, I

• An example of surface coupling represents also the

imposing of theoretical solution (Stokes 5th-order wave,

Pierson-Moskwoitz or Jon-Swap irregular long-crested

waves, superposition of linear waves…) at an inlet

boundary.

• The imposed inlet values can also come from another

numerical solution in the upstream subdomain.

• The problem: reflection of upstream-traveling waves at

such an inlet boundary if the coupling is only one-way.

Surface Coupling, II

• An example of two-way surface coupling:

The upstream domain imposes at interface inlet condition

for the downstream domain;

The downstream domain imposes at interface pressure-

outlet condition for the upstream domain.

• The most comprehensive approach:

Solving for the same variables in the whole domain

simultaneously (as we do with overset grids)…

This fully-implicit approach requires exchange of

information at each iteration within a time step…

… and imposes some compatibility conditions…

Surface Coupling, III

• Instead of using contiguous subdomains and coupling at

a common surface interface, one can also use

overlapping subdomains and enforce coupling over a

volume zone…

• The forcing is realized via a source term of the form:

S* = - µf (ϕ - ϕ*)

where µf is the forcing coefficient.

• A large number is used when the variable value is to be

fixed to ϕ* (e.g. dissipation rate at a near-wall cell).

Volume Coupling, I

• A smoothly varying forcing coefficient provides also a damping function…

• The volume coupling can also be either one-way or two-way (the forcing zones usually do not coincide)…

Volume Coupling, II

µf 3D Navier-Stokes

2D Euler

Forcing zone

• If the grids do not coincide, volume coupling requires

interpolation of one solution to the other grid (mapping).

• If the grid moves, this mapping has to be done in each

time step…

• … or even in each iteration, in the case of DFBI…

• Volume mapping can thus be expensive!

Volume Coupling, III

Example from Technip, I

t = -17.33 s

t = 0 s

t = 1.16 s

Solution domain

for 3D RANSE

computation

Solution domain for 2D Euler

computation

• 3D-RANSE computation is performed only over the time

0 – 1.5 s in a domain 2 m long and 1 m wide around the

cylinder.

• 2D solution of Euler equations to obtain the desired wave

at the cylinder position is performed over a 20 times

longer solution domain (> 100 m) and over 20 times

longer time period (ca. 20 s).

• 2D Euler solution is used to initialize RANSE computation

at the desired time, ignoring the obstacle (as we do with

theoretical wave solutions).

• Mapping 2D solution to 3D domain is much less

expensive than 3D to 3D…

Example from Technip, II

• Theoretical solutions can also be used for volume

coupling…

• Instead of specifying inlet conditions based on theory,

one can use a forcing zone to impose theoretical solution

in any part of the solution domain.

• The advantage of this approach is that it provides

damping both upstream and downstream of obstacles.

• The disadvantage is that theory may not be a good

representation of the solution of Navier-Stokes equations

(e.g. linear wave theory)…

Coupling to Theory, I

• Example: Stokes 5th-order wave theory imposed at both inlet and outlet over forcing zones of different length…

• Note: The computed wavelength is slightly shorter than theoretical, but the solution is forced to theory over a short distance (the forcing coefficient is too strong).

Coupling to Theory, II

Blue: Stokes theory (5th order)

Red: Computed

Forcing zone Forcing zone

Coupling to Theory, III

• 3D example: Flow around a vertical cylinder

• The cylinder disturbs the free surface; disturbances propagate in

all directions.

• Inlet is relatively near cylinder – reflections can be better

observed…

• The solution domain is 9.2 m long and 6.4 m wide; cylinder

diameter is 1 m and its axis is 3.8 m away from inlet.

• Stokes wave parameters: wavelength 3.2 m, wave height 0.2 m,

wave period 1.4043 s

• The mesh is locally refined in free-surface zone and around

cylinder (80 cells per wavelength and 20 cells per wave height).

Forcing is applied all around cylinder…

Coupling to Theory, IV

Grid in the free surface and the value of the forcing coefficient µ0: red means

RANS-zone, blue means maximum forcing to Stokes 5th-order theory. Outside

zone around cylinder, the grid is only fine in x- and z-direction to resolve free

surface variation – in y-direction it is coarse since the wave is long-crested.

2.4 m 1.2 m

1.6 m

1.6 m

Coupling to Theory, V

Grid in the longitudinal section through the solution domain, also showing

volume fraction distribution after 4 periods.

Coupling to Theory, VI

Volume fraction of water in the longitudinal section through the solution

domain, also showing the free surface shape from Stokes 5th-order theory,

after 4 periods. Note that the computed free surface position corresponds to

the theory within forcing zones.

Forcing Forcing

Coupling to Theory, VII

Volume fraction of water in the symmetry plane (upper) and side boundary (lower),

also showing the free surface shape from Stokes 5th-order theory, after 4 periods.

Note that the computed free surface near inlet does not correspond to the theory,

due to reflections.

Computation using standard approach in

STAR-CCM+ (inlet + damping at outlet,

symmetry conditions at sides)

Coupling to Theory, VIII Computation using inlet,

damping at outlet, symmetry

at sides

Computation using forcing

(at inlet, sides and outlet) Free surface

after 4 periods

(around cylinder

it looks the

same)

Disturbances due to

reflections at symmetry

and inlet

No obvious

disturbances

Coupling to Theory, IX

Animation of simulated free surface motion during the 3rd and the 4th period (using

forcing). Along boundaries the free surface position corresponds to Stokes 5th-order

wave theory.

Coupling to Theory, X

Animation of simulated free surface motion during the 3rd and the 4th period using the

standard approach (inlet condition from Stokes 5th-order theory, side boundaries are

symmetry planes, outlet is pressure boundary set to represent flat free surface and

damping is applied over 2.4 m towards outlet).

Coupling to Other Solutions, I

• 2D example: Laminar flow of water around a circular cylinder in a

channel, Reynolds number 200.

• Boundary conditions: steady uniform flow at inlet, constant

pressure at outlet.

• Vortices are shed by the cylinder; pressure-outlet boundary

condition is not optimal for outgoing vortices – disturbances

occur…

• The solution is forced into channel flow without obstacle over

some distance towards outlet.

• The aim of coupling to undisturbed channel flow is to avoid

disturbances at outlet, i.e. to obtain an almost steady flow at

outlet.

Coupling to Other Solutions, II

2D grid for the computation of unsteady laminar flow around cylinder in a channel

(only part of the solution domain is shown – it is longer both upstream and

downstream, with grid structure similar to what is seen here at both ends).

The grid has 180 cells along cylinder perimeter and the thickness of the first cell next

to wall is 1/166th of the cylinder diameter. The time step was set to 120 steps per

period of lift oscillation (on average 60 steps per period of drag oscillation). Under-

relaxation factors were 1.0 for all transport equations and 0.5 for pressure.

Coupling to Other Solutions, III

No forcing

Forcing

Drag force on cylinder: the result is practically identical, i.e. the forcing of the flow far

away from cylinder does not influence the flow around cylinder (as far as drag and lift

are concerned).

Coupling to Other Solutions, IV

Animation of pressure variation: no forcing (upper) and with forcing (lower)

Coupling to Other Solutions, V

Animation of velocity variation: no forcing (upper) and with forcing (lower)

Future Developments

• Future developments of STAR-CCM+ will include:

The possibility to apply the method described in this

presentation as a feature rather than field function coding:

• Coupling to theories available in STAR-CCM+ over some

distance to boundary (as is the case with wave dumping

currently);

• Coupling to 2D simulations of undisturbed flow running

simultaneously in another region (providing the solution without

obstacle).

Generic API for surface coupling at selected boundaries;

Generic API for volume coupling over selected zone(s).