3D Dam Break

The breaking dam free surface problem. This code demonstrates the basic usage of the free surface module in Palabos.

Free Surface Model

Free-surface simulations are characterized by the fact that the discrete cells of the flow domain dynamically change their physical state by getting filled or emptied due to the movement of the liquid that is simulated. In order to keep track of the different states of the cells, a cell type is assigned to each cell, allowing to distinguish between obstacle (O), fluid (F), empty (gas, G), and interface (I). Cells are regarded to be of fluid or gas type.

As the amount of fluid in the cells may vary over time, one keeps track of the mass flux between neighboring cells by measuring the mass exchange $\Delta m_i(\boldsymbol x, t + 1)$ arising from the incoming and outgoing populations $f_i(\boldsymbol x, t)$ and $f_{inv(i)}(\boldsymbol x+\vec{e_i}, t)$ at the lattice node $\boldsymbol x$: $$ \Delta m_i(\boldsymbol x, t + 1)=A_i \cdot (f_{inv(i)}(\boldsymbol x+\vec{e_i}, t)-f_i(\boldsymbol x, t)) $$ where $A_i$ is the fluid exchange area between both cells. Its value is approximated depending on the types of the neighboring cells and their fluid fractions. The total mass of the cell for the next timestep is thus determined by the mass of the current timestep $m(\boldsymbol x, t)$ and the sum over all mass fluxes $\Delta m_i(\boldsymbol x, t + 1)$; the fluid fraction is updated respectively and a reflagging of the cell types becomes necessary before the next timestep as depicted in Figure 1. Filled cells are flagged to F, emptied cells to G and partially filled cells to I. Afterwards, a closed layer of interface cells needs to be constructed between gas and liquid phase in order to retain a valid domain configuration, as shown in Figure 1 (A)-(C).

Free Surface Model Illustration

Codes Decoding:

The surfaceTensionLB can be computed as:

    surfaceTensionLB = rhoEmpty * gLB * N * N / Bo;

For this problem, we need to specific the cells that are fluid, wall (dam part), and empty (void).

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21


// Specifies the initial condition for the fluid (each cell is assigned the
// flag "fluid", "empty", or "wall").
int initialFluidFlags(plint iX, plint iY, plint iZ) {
    // Place an obstacle on the left end, which is hit by the fluid.
    bool insideObstacle =
        iX >= obstacleCenterXYplane-obstacleWidth/2 &&
        iX <= obstacleCenterXYplane+obstacleWidth/2 &&
        iY >= ny/2-obstacleLength/2 &&
        iY <= ny/2+obstacleLength/2 &&
        iZ <= obstacleHeight+1;
    
    if (insideObstacle) {
        return freeSurfaceFlag::wall;
    }
    else if (iX >= beginWaterReservoir && iZ <= waterReservoirHeight) {
        return freeSurfaceFlag::fluid;
    }
    else {
        return freeSurfaceFlag::empty;
    }
}

For the problem, we need several parameter for the simulation, which include kinematic viscosity, bond number, contact angle, number of lattice nodes for lz, delta_t, and maxIter.

For a simulation in a desktop computer, $\nu=1.e-5 (m^2/s)$, $ Bo = 100$, $Contact Angle=80.0 ^\circ $, $N_{lz}=40$, $\delta_t=1.e-3$, and the $maxIter=80000$

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29


    if (global::argc() != 8) {
        pcout << "Error missing some input parameter\n";
    }

    try {
        global::argv(1).read(outDir);
        global::directories().setOutputDir(outDir+"/");

        global::argv(2).read(nuPhys);
        global::argv(3).read(Bo);
        global::argv(4).read(contactAngle);
        global::argv(5).read(N);
        global::argv(6).read(delta_t);
        global::argv(7).read(maxIter);
    }
    catch(PlbIOException& except) {
        pcout << except.what() << std::endl;
        pcout << "The parameters for this program are :\n";
        pcout << "1. Output directory name.\n";
        pcout << "2. kinematic viscosity in physical Units (m^2/s) .\n";
        pcout << "3. Bond number (Bo = rho * g * L^2 / gamma).\n";
        pcout << "4. Contact angle (in degrees).\n";
        pcout << "5. number of lattice nodes for lz .\n";
        pcout << "6. delta_t .\n"; 
        pcout << "7. maxIter .\n";
        pcout << "Reasonable parameters on a desktop computer are: " << (std::string)global::argv(0) << " tmp 1.e-5 100 80.0 40 1.e-3 80000\n";
        pcout << "Reasonable parameters on a parallel machine are: " << (std::string)global::argv(0) << " tmp 1.e-6 100 80.0 100 1.e-4 80000\n";
        exit (EXIT_FAILURE);
    }

The results with $maxIter=20000$ are displayed as:

Output at ITERNATION=1980 and ITERNATION=2000

Simulation Output

GIF animation of density changes:

Density change

GIF animation of flow velocity:

Velocity

GIF animation of VOF:

Volume of Fraction

Full Codes:

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268


/* This file is part of the Palabos library.
 *
 * The Palabos softare is developed since 2011 by FlowKit-Numeca Group Sarl
 * (Switzerland) and the University of Geneva (Switzerland), which jointly
 * own the IP rights for most of the code base. Since October 2019, the
 * Palabos project is maintained by the University of Geneva and accepts
 * source code contributions from the community.
 * 
 * Contact:
 * Jonas Latt
 * Computer Science Department
 * University of Geneva
 * 7 Route de Drize
 * 1227 Carouge, Switzerland
 * jonas.latt@unige.ch
 *
 * The most recent release of Palabos can be downloaded at 
 * <https://palabos.unige.ch/>
 *
 * The library Palabos is free software: you can redistribute it and/or
 * modify it under the terms of the GNU Affero General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * The library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

/* The breaking dam free surface problem. This code demonstrates the basic usage of the
 * free surface module in Palabos. Surface tension and contact angles are optional. 
 */

#include "palabos3D.h"
#include "palabos3D.hh"

using namespace plb;

#define DESCRIPTOR descriptors::ForcedD3Q19Descriptor

typedef double T;


// Smagorinsky constant for LES model.
const T cSmago = 0.14;

// Physical dimensions of the system (in meters).
const T lx = 3.22;
const T ly = 1.0;
const T lz = 1.0;

const T rhoEmpty = T(1);
    
plint writeImagesIter   = 100;
plint getStatisticsIter = 20;

plint maxIter;
plint N;
plint nx, ny, nz;
T delta_t, delta_x;
Array<T,3> externalForce;
T nuPhys, nuLB, tau, omega, Bo, surfaceTensionLB, contactAngle;

std::string outDir;
plint obstacleCenterXYplane, obstacleLength, obstacleWidth, obstacleHeight, beginWaterReservoir, waterReservoirHeight;
plint waterLevelOne, waterLevelTwo, waterLevelThree, waterLevelFour;

void setupParameters() {
    delta_x = lz / N;
    nx = util::roundToInt(lx / delta_x);
    ny = util::roundToInt(ly / delta_x);
    nz = util::roundToInt(lz / delta_x);

    // Gravity in lattice units.
    T gLB = 9.8 * delta_t * delta_t/delta_x;
    externalForce = Array<T,3>(0., 0., -gLB);
    tau            = (nuPhys*DESCRIPTOR<T>::invCs2*delta_t)/(delta_x*delta_x) + 0.5;
    omega          = 1./tau;    
    nuLB           = (tau-0.5)*DESCRIPTOR<T>::cs2; // Viscosity in lattice units.
    
    surfaceTensionLB = rhoEmpty * gLB * N * N / Bo;

    obstacleCenterXYplane = util::roundToInt(0.744*N);
    obstacleLength        = util::roundToInt(0.403*N);
    obstacleWidth         = util::roundToInt(0.161*N);
    obstacleHeight        = util::roundToInt(0.161*N);
    beginWaterReservoir   = util::roundToInt((0.744+1.248)*N);
    waterReservoirHeight  = util::roundToInt(0.55*N);
    
    waterLevelOne   = util::roundToInt(0.496*N);
    waterLevelTwo   = util::roundToInt(2.*0.496*N);
    waterLevelThree = util::roundToInt(3.*0.496*N);
    waterLevelFour  = util::roundToInt((3.*0.496 + 1.150)*N);
}

// Specifies the initial condition for the fluid (each cell is assigned the
// flag "fluid", "empty", or "wall").
int initialFluidFlags(plint iX, plint iY, plint iZ) {
    // Place an obstacle on the left end, which is hit by the fluid.
    bool insideObstacle =
        iX >= obstacleCenterXYplane-obstacleWidth/2 &&
        iX <= obstacleCenterXYplane+obstacleWidth/2 &&
        iY >= ny/2-obstacleLength/2 &&
        iY <= ny/2+obstacleLength/2 &&
        iZ <= obstacleHeight+1;
    
    if (insideObstacle) {
        return freeSurfaceFlag::wall;
    }
    else if (iX >= beginWaterReservoir && iZ <= waterReservoirHeight) {
        return freeSurfaceFlag::fluid;
    }
    else {
        return freeSurfaceFlag::empty;
    }
}

void writeResults(MultiBlockLattice3D<T,DESCRIPTOR>& lattice, MultiScalarField3D<T>& volumeFraction, plint iT)
{
    static const plint nx = lattice.getNx();
    static const plint ny = lattice.getNy();
    static const plint nz = lattice.getNz();
    Box3D slice(0, nx-1, ny/2, ny/2, 0, nz-1);
    ImageWriter<T> imageWriter("leeloo");
    imageWriter.writeScaledGif(createFileName("u", iT, 6),
                               *computeVelocityNorm(lattice, slice)); 

    imageWriter.writeScaledGif(createFileName("rho", iT, 6),
                               *computeDensity(lattice, slice));
                   
    imageWriter.writeScaledGif(createFileName("volumeFraction", iT, 6), *extractSubDomain(volumeFraction, slice));

    // Use a marching-cube algorithm to reconstruct the free surface and write an STL file.
    std::vector<T> isoLevels;
    isoLevels.push_back((T) 0.5);
    typedef TriangleSet<T>::Triangle Triangle;
    std::vector<Triangle> triangles;
    isoSurfaceMarchingCube(triangles, volumeFraction, isoLevels, volumeFraction.getBoundingBox());
    TriangleSet<T>(triangles).writeBinarySTL(createFileName(outDir+"/interface", iT, 6)+".stl");

    VtkImageOutput3D<T> vtkOut(createFileName("volumeFraction", iT, 6), 1.);
    vtkOut.writeData<float>(volumeFraction, "vf", 1.);
}

void writeStatistics(FreeSurfaceFields3D<T,DESCRIPTOR>& fields) {
    pcout << " -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- " << std::endl;
    T averageMass = freeSurfaceAverageMass<T,DESCRIPTOR>(fields.freeSurfaceArgs, fields.lattice.getBoundingBox());
    pcout << "Average Mass: " << averageMass  << std::endl;
    T averageDensity = freeSurfaceAverageDensity<T,DESCRIPTOR>(fields.freeSurfaceArgs, fields.lattice.getBoundingBox());
    pcout << "Average Density: " << std::setprecision(12) << averageDensity  << std::endl;

    T averageVolumeFraction = freeSurfaceAverageVolumeFraction<T,DESCRIPTOR>(fields.freeSurfaceArgs, fields.lattice.getBoundingBox());
    pcout << "Average Volume-Fraction: " << std::setprecision(12) << averageVolumeFraction  << std::endl;

    pcout << " -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- " << std::endl;
}


int main(int argc, char **argv)
{
    plbInit(&argc, &argv);
    global::directories().setInputDir("./");
        
    if (global::argc() != 8) {
        pcout << "Error missing some input parameter\n";
    }

    try {
        global::argv(1).read(outDir);
        global::directories().setOutputDir(outDir+"/");

        global::argv(2).read(nuPhys);
        global::argv(3).read(Bo);
        global::argv(4).read(contactAngle);
        global::argv(5).read(N);
        global::argv(6).read(delta_t);
        global::argv(7).read(maxIter);
    }
    catch(PlbIOException& except) {
        pcout << except.what() << std::endl;
        pcout << "The parameters for this program are :\n";
        pcout << "1. Output directory name.\n";
        pcout << "2. kinematic viscosity in physical Units (m^2/s) .\n";
        pcout << "3. Bond number (Bo = rho * g * L^2 / gamma).\n";
        pcout << "4. Contact angle (in degrees).\n";
        pcout << "5. number of lattice nodes for lz .\n";
        pcout << "6. delta_t .\n"; 
        pcout << "7. maxIter .\n";
        pcout << "Reasonable parameters on a desktop computer are: " << (std::string)global::argv(0) << " tmp 1.e-5 100 80.0 40 1.e-3 80000\n";
        pcout << "Reasonable parameters on a parallel machine are: " << (std::string)global::argv(0) << " tmp 1.e-6 100 80.0 100 1.e-4 80000\n";
        exit (EXIT_FAILURE);
    }
    
    setupParameters();
    
    pcout << "delta_t= " << delta_t << std::endl;
    pcout << "delta_x= " << delta_x << std::endl;
    pcout << "delta_t*delta_t/delta_x= " << delta_t*delta_t/delta_x << std::endl;
    pcout << "externalForce= " << externalForce[2] << std::endl;
    pcout << "relaxation time= " << tau << std::endl;
    pcout << "omega= " << omega << std::endl;
    pcout << "kinematic viscosity physical units = " << nuPhys << std::endl;
    pcout << "kinematic viscosity lattice units= " << nuLB << std::endl;
    
    global::timer("initialization").start();
    

    SparseBlockStructure3D blockStructure(createRegularDistribution3D(nx, ny, nz));

    Dynamics<T,DESCRIPTOR>* dynamics
        = new SmagorinskyBGKdynamics<T,DESCRIPTOR>(omega, cSmago);

    // If surfaceTensionLB is 0, then the surface tension algorithm is deactivated.
    // If contactAngle is less than 0, then the contact angle algorithm is deactivated.
    FreeSurfaceFields3D<T,DESCRIPTOR> fields( blockStructure, dynamics->clone(), rhoEmpty,
                                              surfaceTensionLB, contactAngle, externalForce );
    //integrateProcessingFunctional(new ShortenBounceBack3D<T,DESCRIPTOR>, fields.lattice.getBoundingBox(), fields.freeSurfaceArgs, 0);

    // Set all outer-wall cells to "wall" (here, bulk-cells are also set to "wall", but it
    // doesn't matter, because they are overwritten on the next line).
    setToConstant(fields.flag, fields.flag.getBoundingBox(), (int)freeSurfaceFlag::wall);
    // In the bulk (all except outer wall layer), initialize the flags as specified by
    // the function "initialFluidFlags".
    setToFunction(fields.flag, fields.flag.getBoundingBox().enlarge(-1), initialFluidFlags);
    
    fields.defaultInitialize();

    pcout << "Time spent for setting up lattices: "
          << global::timer("initialization").stop() << std::endl;
    T lastIterationTime = T();

    for (plint iT = 0; iT <= maxIter; ++iT) {
        global::timer("iteration").restart();
        
        T sum_of_mass_matrix = T();
        T lost_mass = T();
        if (iT % getStatisticsIter==0) {
            pcout << std::endl;
            pcout << "ITERATION = " << iT << std::endl;
            pcout << "Time of last iteration is " << lastIterationTime << " seconds" << std::endl;
            writeStatistics(fields);
            sum_of_mass_matrix = fields.lattice.getInternalStatistics().getSum(0);
            pcout << "Sum of mass matrix: " << sum_of_mass_matrix << std::endl;
            lost_mass = fields.lattice.getInternalStatistics().getSum(1);
            pcout << "Lost mass: " << lost_mass << std::endl;
            pcout << "Total mass: " << sum_of_mass_matrix + lost_mass << std::endl;
            pcout << "Interface cells: " << fields.lattice.getInternalStatistics().getIntSum(0) << std::endl;
        }

        if (iT % writeImagesIter == 0) {
            global::timer("images").start();
            writeResults(fields.lattice, fields.volumeFraction, iT);
            pcout << "Total time spent for writing images: "
                << global::timer("images").stop() << std::endl;
        }                           

        // This includes the collision-streaming cycle, plus all free-surface operations.
        fields.lattice.executeInternalProcessors();
        fields.lattice.evaluateStatistics();
        fields.lattice.incrementTime();

        lastIterationTime = global::timer("iteration").stop();
    }
}

GIF Animation Generation Code

1

gifsicle --colors 256 --loop *.gif > anim.gif

Reference

[1] \palabos\examples\codesByTopic\shanChenMultiPhase\segregation2D.cpp

[2] Schreiber, M., Neumann, P., Zimmer, S., & Bungartz, H. J. (2011). Free-surface lattice-Boltzmann simulation on many-core architectures. Procedia Computer Science, 4, 984-993.