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## 2.3 Breaking of a dam

In this tutorial we shall solve a problem of simplified dam break in 2 dimensions using the interFoam.The feature of the problem is a transient flow of two fluids separated by a sharp interface, or free surface. The two-phase algorithm in interFoam is based on the volume of fluid (VOF) method in which a specie transport equation is used to determine the relative volume fraction of the two phases, or phase fraction , in each computational cell. Physical properties are calculated as weighted averages based on this fraction. The nature of the VOF method means that an interface between the species is not explicitly computed, but rather emerges as a property of the phase fraction field. Since the phase fraction can have any value between 0 and 1, the interface is never sharply defined, but occupies a volume around the region where a sharp interface should exist.

The test setup consists of a column of water at rest located behind a membrane on the left side of a tank. At time , the membrane is removed and the column of water collapses. During the collapse, the water impacts an obstacle at the bottom of the tank and creates a complicated flow structure, including several captured pockets of air. The geometry and the initial setup is shown in Figure 2.21.

### 2.3.1 Mesh generation

The user should go to their run directory and copy the damBreak case from the \$FOAM_TUTORIALS/multiphase/interFoam/laminar/damBreak directory, i.e.

run
cp -r \$FOAM_TUTORIALS/multiphase/interFoam/laminar/damBreak/damBreak .
Go into the damBreak case directory and generate the mesh running blockMesh as described previously. The damBreak mesh consist of 5 blocks; the blockMeshDict entries are given below.
17convertToMeters 0.146;
18
19vertices
20(
21    (0 0 0)
22    (2 0 0)
23    (2.16438 0 0)
24    (4 0 0)
25    (0 0.32876 0)
26    (2 0.32876 0)
27    (2.16438 0.32876 0)
28    (4 0.32876 0)
29    (0 4 0)
30    (2 4 0)
31    (2.16438 4 0)
32    (4 4 0)
33    (0 0 0.1)
34    (2 0 0.1)
35    (2.16438 0 0.1)
36    (4 0 0.1)
37    (0 0.32876 0.1)
38    (2 0.32876 0.1)
39    (2.16438 0.32876 0.1)
40    (4 0.32876 0.1)
41    (0 4 0.1)
42    (2 4 0.1)
43    (2.16438 4 0.1)
44    (4 4 0.1)
45);
46
47blocks
48(
49    hex (0 1 5 4 12 13 17 16) (23 8 1) simpleGrading (1 1 1)
50    hex (2 3 7 6 14 15 19 18) (19 8 1) simpleGrading (1 1 1)
51    hex (4 5 9 8 16 17 21 20) (23 42 1) simpleGrading (1 1 1)
52    hex (5 6 10 9 17 18 22 21) (4 42 1) simpleGrading (1 1 1)
53    hex (6 7 11 10 18 19 23 22) (19 42 1) simpleGrading (1 1 1)
54);
55
56edges
57(
58);
59
60boundary
61(
62    leftWall
63    {
64        type wall;
65        faces
66        (
67            (0 12 16 4)
68            (4 16 20 8)
69        );
70    }
71    rightWall
72    {
73        type wall;
74        faces
75        (
76            (7 19 15 3)
77            (11 23 19 7)
78        );
79    }
80    lowerWall
81    {
82        type wall;
83        faces
84        (
85            (0 1 13 12)
86            (1 5 17 13)
87            (5 6 18 17)
88            (2 14 18 6)
89            (2 3 15 14)
90        );
91    }
92    atmosphere
93    {
94        type patch;
95        faces
96        (
97            (8 20 21 9)
98            (9 21 22 10)
99            (10 22 23 11)
100        );
101    }
102);
103
104mergePatchPairs
105(
106);
107
108// ************************************************************************* //

### 2.3.2 Boundary conditions

The user can examine the boundary geometry generated by blockMesh by viewing the boundary file in the constant/polyMesh directory. The file contains a list of 5 boundary patches: leftWall, rightWall, lowerWall, atmosphere and defaultFaces. The user should notice the type of the patches. The atmosphere is a standard patch, i.e. has no special attributes, merely an entity on which boundary conditions can be specified. The defaultFaces patch is empty since the patch normal is in the direction we will not solve in this 2D case. The leftWall, rightWall and lowerWall patches are each a wall.

Like the generic patch, the wall type contains no geometric or topological information about the mesh and only differs from the plain patch in that it identifies the patch as a wall, should an application need to know, e.g. to apply special wall surface modelling. For example, the interFoam solver includes modelling of surface tension and can include wall adhesion at the contact point between the interface and wall surface. Wall adhesion models can be applied through a special boundary condition on the alpha () field, e.g.  the constantAlphaContactAngle boundary condition, which requires the user to specify a static contact angle, theta0.

In this tutorial we would like to ignore surface tension effects between the wall and interface. We can do this by setting the static contact angle, . However, rather than using the constantAlphaContactAngle boundary condition, the simpler zeroGradient can be applied to alpha on the walls.

The top boundary is free to the atmosphere so needs to permit both outflow and inflow according to the internal flow. We therefore use a combination of boundary conditions for pressure and velocity that does this while maintaining stability. They are:

• totalPressure which is a fixedValue condition calculated from specified total pressure p0 and local velocity U;
• pressureInletOutletVelocity, which applies zeroGradient on all components, except where there is inflow, in which case a fixedValue condition is applied to the tangential component;
• inletOutlet, which is a zeroGradient condition when flow outwards, fixedValue when flow is inwards.

At all wall boundaries, the fixedFluxPressure boundary condition is applied to the pressure field, which adjusts the pressure gradient so that the boundary flux matches the velocity boundary condition for solvers that include body forces such as gravity and surface tension.

The defaultFaces patch representing the front and back planes of the 2D problem, is, as usual, an empty type.

### 2.3.3 Setting initial field

Unlike the previous cases, we shall now specify a non-uniform initial condition for the phase fraction where

 (2.15)
This will be done by running the setFields utility. It requires a setFieldsDict dictionary, located in the system directory, whose entries for this case are shown below.
17
18defaultFieldValues
19(
20    volScalarFieldValue alpha.water 0
21);
22
23regions
24(
25    boxToCell
26    {
27        box (0 0 -1) (0.1461 0.292 1);
28        fieldValues
29        (
30            volScalarFieldValue alpha.water 1
31        );
32    }
33);
34
35
36// ************************************************************************* //

The defaultFieldValues sets the default value of the fields, i.e. the value the field takes unless specified otherwise in the regions sub-dictionary. That sub-dictionary contains a list of subdictionaries containing fieldValues that override the defaults in a specified region. The region creates a set of points, cells or faces based on some topological constraint. Here, boxToCell creates a bounding box within a vector minimum and maximum to define the set of cells of the water region. The phase fraction is defined as 1 in this region.

The setFields utility reads fields from file and, after re-calculating those fields, will write them back to file. In the damBreak tutorial, the alpha.water field is initially stored as a backup named alpha.water.orig. A field file with the .orig extension is read in when the actual file does not exist, so setFields will read alpha.water.orig but write the resulting output to alpha.water (or alpha.water.gz if compression is switched on). This way the original file is not overwritten, so can be reused.

The user should therefore execute setFields like any other utility by:

setFields
Using paraFoam, check that the initial alpha.water field corresponds to the desired distribution as in Figure 2.22.

### 2.3.4 Fluid properties

Let us examine the transportProperties file in the constant directory. The dictionary first contains the names of each fluid phase in the phases list, here water and air. The material properties for each fluid are then separated into two dictionaries water and air. The transport model for each phase is selected by the transportModel keyword. The user should select Newtonian in which case the kinematic viscosity is single valued and specified under the keyword nu. The viscosity parameters for other models, e.g. CrossPowerLaw, would otherwise be specified as described in section 7.3. The density is specified under the keyword rho.

The surface tension between the two phases is specified by the keyword sigma. The values used in this tutorial are listed in Table 2.3.

 water properties Kinematic viscosity nu Density rho air properties Kinematic viscosity nu Density rho 1.0 Properties of both phases Surface tension sigma 0.07
Table 2.3: Fluid properties for the damBreak tutorial

Gravitational acceleration is uniform across the domain and is specified in a file named g in the constant directory. Unlike a normal field file, e.g.  U and p, g is a uniformDimensionedVectorField and so simply contains a set of dimensions and a value that represents for this tutorial:

17
18dimensions      [0 1 -2 0 0 0 0];
19value           (0 -9.81 0);
20
21
22// ************************************************************************* //

### 2.3.5 Turbulence modelling

As in the cavity example, the choice of turbulence modelling method is selectable at run-time through the simulationType keyword in turbulenceProperties dictionary. In this example, we wish to run without turbulence modelling so we set laminar:

17
18simulationType  laminar;
19
20
21// ************************************************************************* //

### 2.3.6 Time step control

Time step control is an important issue in transient simulation and the surface-tracking algorithm in interface capturing solvers. The Courant number needs to be limited depending on the choice of algorithm: with the “explicit” MULES algorithm, an upper limit of for stability is typical in the region of the interface; but with “semi-implicit” MULES, specified by the MULESCorr keyword in the fvSolution file, there is really no upper limit in for stability, but instead the level is determined by requirements of temporal accuracy.

In general it is difficult to specify a fixed time-step to satisfy the criterion, so interFoam offers automatic adjustment of the time step as standard in the controlDict. The user should specify adjustTimeStep to be on and the the maximum for the phase fields, maxAlphaCo, and other fields, maxCo, to be 1.0. The upper limit on time step maxDeltaT can be set to a value that will not be exceeded in this simulation, e.g.  1.0.

By using automatic time step control, the steps themselves are never rounded to a convenient value. Consequently if we request that OpenFOAM saves results at a fixed number of time step intervals, the times at which results are saved are somewhat arbitrary. However even with automatic time step adjustment, OpenFOAM allows the user to specify that results are written at fixed times; in this case OpenFOAM forces the automatic time stepping procedure to adjust time steps so that it ‘hits’ on the exact times specified for write output. The user selects this with the adjustableRunTime option for writeControl in the controlDict dictionary. The controlDict dictionary entries should be:

17
18application     interFoam;
19
20startFrom       startTime;
21
22startTime       0;
23
24stopAt          endTime;
25
26endTime         1;
27
28deltaT          0.001;
29
31
32writeInterval   0.05;
33
34purgeWrite      0;
35
36writeFormat     binary;
37
38writePrecision  6;
39
40writeCompression off;
41
42timeFormat      general;
43
44timePrecision   6;
45
46runTimeModifiable yes;
47
49
50maxCo           1;
51maxAlphaCo      1;
52
53maxDeltaT       1;
54
55
56// ************************************************************************* //

### 2.3.7 Discretisation schemes

The interFoam solver uses the multidimensional universal limiter for explicit solution (MULES) method, created by Henry Weller, to maintain boundedness of the phase fraction independent of underlying numerical scheme, mesh structure, etc. The choice of schemes for convection are therfore not restricted to those that are strongly stable or bounded, e.g. upwind differencing.

The convection schemes settings are made in the divSchemes sub-dictionary of the fvSchemes dictionary. In this example, the convection term in the momentum equation (), denoted by the div(rhoPhi,U) keyword, uses Gauss linearUpwind grad(U) to produce good accuracy. Here, we have opted for best stability with . The term, represented by the div(phi,alpha) keyword uses the vanLeer scheme. The term, represented by the div(phirb,alpha) keyword, can use second order linear (central) differencing as boundedness is assured by the MULES algorithm.

The other discretised terms use commonly employed schemes so that the fvSchemes dictionary entries should therefore be:

17
18ddtSchemes
19{
20    default         Euler;
21}
22
24{
25    default         Gauss linear;
26}
27
28divSchemes
29{
31    div(phi,alpha)  Gauss vanLeer;
32    div(phirb,alpha) Gauss linear;
34}
35
36laplacianSchemes
37{
38    default         Gauss linear corrected;
39}
40
41interpolationSchemes
42{
43    default         linear;
44}
45
47{
48    default         corrected;
49}
50
51
52// ************************************************************************* //

### 2.3.8 Linear-solver control

In the fvSolution file, the alpha.water sub-dictionary in solvers contains elements that are specific to interFoam. Of particular interest are the nAlphaSubCycles and cAlpha keywords. nAlphaSubCycles represents the number of sub-cycles within the equation; sub-cycles are additional solutions to an equation within a given time step. It is used to enable the solution to be stable without reducing the time step and vastly increasing the solution time. Here we specify 2 sub-cycles, which means that the equation is solved in half length time steps within each actual time step.

The cAlpha keyword is a factor that controls the compression of the interface where: 0 corresponds to no compression; 1 corresponds to conservative compression; and, anything larger than 1, relates to enhanced compression of the interface. We generally adopt a value of 1.0 which is employed in this example.

### 2.3.9 Running the code

Running of the code has been described in detail in previous tutorials. Try the following, that uses tee, a command that enables output to be written to both standard output and files:

cd \$FOAM_RUN/damBreak
interFoam | tee log
The code will now be run interactively, with a copy of output stored in the log file.

### 2.3.10 Post-processing

Post-processing of the results can now be done in the usual way. The user can monitor the development of the phase fraction alpha.water in time, e.g.  see Figure 2.23.

### 2.3.11 Running in parallel

The results from the previous example are generated using a fairly coarse mesh. We now wish to increase the mesh resolution and re-run the case. The new case will typically take a few hours to run with a single processor so, should the user have access to multiple processors, we can demonstrate the parallel processing capability of OpenFOAM.

The user should first clone the damBreak case, e.g. by

run
foamCloneCase damBreak damBreakFine
Enter the new case directory and change the blocks description in the blockMeshDict dictionary to

blocks
(
hex (0 1 5 4 12 13 17 16) (46 10 1) simpleGrading (1 1 1)
hex (2 3 7 6 14 15 19 18) (40 10 1) simpleGrading (1 1 1)
hex (4 5 9 8 16 17 21 20) (46 76 1) simpleGrading (1 2 1)
hex (5 6 10 9 17 18 22 21) (4 76 1) simpleGrading (1 2 1)
hex (6 7 11 10 18 19 23 22) (40 76 1) simpleGrading (1 2 1)
);
Here, the entry is presented as printed from the blockMeshDict file; in short the user must change the mesh densities, e.g. the 46 10 1 entry, and some of the mesh grading entries to 1 2 1. Once the dictionary is correct, generate the mesh by running blockMesh.

As the mesh has now changed from the damBreak example, the user must re-initialise the phase field alpha.water in the 0 time directory since it contains a number of elements that is inconsistent with the new mesh. Note that there is no need to change the U and p_rgh fields since they are specified as uniform which is independent of the number of elements in the field. We wish to initialise the field with a sharp interface, i.e. it elements would have or . Updating the field with mapFields may produce interpolated values at the interface, so it is better to rerun the setFields utility.

The mesh size is now inconsistent with the number of elements in the alpha.water.gz file in the 0 directory, so the user must delete that file so that the original alpha.water.orig file is used instead.

rm 0/alpha.water.gz
setFields

The method of parallel computing used by OpenFOAM is known as domain decomposition, in which the geometry and associated fields are broken into pieces and allocated to separate processors for solution. The first step required to run a parallel case is therefore to decompose the domain using the decomposePar utility. There is a dictionary associated with decomposePar named decomposeParDict which is located in the system directory of the tutorial case; also, like with many utilities, a default dictionary can be found in the directory of the source code of the specific utility, i.e. in \$FOAM_UTILITIES/parallelProcessing/decomposePar for this case.

The first entry is numberOfSubdomains which specifies the number of subdomains into which the case will be decomposed, usually corresponding to the number of processors available for the case.

In this tutorial, the method of decomposition should be simple and the corresponding simpleCoeffs should be edited according to the following criteria. The domain is split into pieces, or subdomains, in the , and directions, the number of subdomains in each direction being given by the vector . As this geometry is 2 dimensional, the 3rd direction, , cannot be split, hence must equal 1. The and components of split the domain in the and directions and must be specified so that the number of subdomains specified by and equals the specified numberOfSubdomains, i.e.   numberOfSubdomains. It is beneficial to keep the number of cell faces adjoining the subdomains to a minimum so, for a square geometry, it is best to keep the split between the and directions should be fairly even. The delta keyword should be set to 0.001.

For example, let us assume we wish to run on 4 processors. We would set numberOfSubdomains to 4 and . The user should run decomposePar with:

decomposePar
The terminal output shows that the decomposition is distributed fairly even between the processors.

The user should consult section 3.4 for details of how to run a case in parallel; in this tutorial we merely present an example of running in parallel. We use the openMPI implementation of the standard message-passing interface (MPI). As a test here, the user can run in parallel on a single node, the local host only, by typing:

mpirun -np 4 interFoam -parallel > log &

The user may run on more nodes over a network by creating a file that lists the host names of the machines on which the case is to be run as described in section 3.4.3. The case should run in the background and the user can follow its progress by monitoring the log file as usual.

### 2.3.12 Post-processing a case run in parallel

Once the case has completed running, the decomposed fields and mesh can be reassembled for post-processing using the reconstructPar utility. Simply execute it from the command line. The results from the fine mesh are shown in Figure 2.25. The user can see that the resolution of interface has improved significantly compared to the coarse mesh.

The user may also post-process an individual region of the decomposed domain individually by simply treating the individual processor directory as a case in its own right. For example if the user starts paraFoam by

paraFoam -case processor1
then processor1 will appear as a case module in ParaView. Figure 2.24 shows the mesh from processor 1 following the decomposition of the domain using the simple method.