VolcFlow

VFweb

24 August 2016 : this site is still under reconstruction !

  • last modification: January 2015

    vf_ianis_lr VolcFlow has been developped for the simulation of volcanic flows
    at the Laboratoire Magmas et Volcans, Clermont-Ferrand
    by Karim Kelfoun (k.kelfoun @ opgc.univ-bpclermont.fr) and collaborators.

    VolcFlow has been be used:

    • for determining the rheological behaviour of dense pyroclastic flows and debris avalanches
    • for visualizing deformations of the surface of debris avalanche and interpret or compare with field structures
    • for volcanic hazard mapping
    • for the the simulation of tsunami generated by volcanic flows
    • for reproducing the emplacement of fluidized flows in laboratory
    • for the simulation of lava flows
    • for the simulation of dense and dilute pyroclastic flows

    Soc

    Simulation of Socompa avalanche, Kelfoun and Druitt, 2005

    More than 100 users worldwide (in 2015)

     

     

  • 2. Theory

    VolcFlow is based on the depth-average approximation. Using a topography-linked co-ordinate system, with x and y parallel to the local ground surface and hperpendicular to it, the general depth-averaged equations of mass and momentum conservation are:schem_num

    with:

    resistf

    kactpass

    The equations were solved using an original shock-capturing numerical method based on a simple or a double upwind Eulerian scheme (fixed by the user). The schemes can handle shocks, rarefaction waves and granular jumps, and are very stable even on complex topography and on both numerically ‘wet’ and ‘dry’ surfaces. (Some numerical schemes require the ground ahead of the avalanche to be covered with a very thin artificial layer of avalanche material: a so-called numerically ‘wet’ surface (Toro, 2001) ).

     

    For the multifluid version, similar set of equations are solve simultaneously, together with interaction laws.

    VolcFlow can take into account frictional (with one or two friction angles), viscous, Bingham, Voellmy, etc…as well as user-defined behaviours.

     

    For more details on the equations and the numerical scheme:

    Kelfoun K. and T.H. Druitt, 2005, Numerical modelling of the emplacement of the 7500 BP Socompa rock avalanche, Chile. J. Geophys. Res., B12202, doi : 10.1029/2005JB003758, 2005.

    Kelfoun K., Giachetti T. and Labazuy P., 2010, Landslide–generated tsunamis at Réunion Island, J. Geophys. Res., Earth Surface, doi:10.1029/2009JF001381.

    Kelfoun K., 2011, Suitability of simple rheological laws for the numerical simulation of dense pyroclastic flows and long-runout volcanic avalanches, J. Geophys. Res., Solid Earth, doi:10.1029/ 2010JB007622.

     

     

  • 3. The one-fluid version

    The distributed version of VolcFlow is isothermal and simulates one fluid.
    It has been used for the simulation of granular flows in laboratory, debris avalanches, lahars and dense pyroclastic flows.
    Users can use predefined rheologies as weel as their own rheological laws compatible with the depth averaged approach.Sedimentation and erosion can be simulated too.

    3.1 Simulation of debris avalanches

    soc1 soc2
    soc3 soc4

    Simulation of Socompa debris avalanche (details on the natural deposits of Socompa avalanche).
    See the movie file (7.7 Mo)
    Read the following paper for further details:
    Kelfoun K, Druitt TH (2005) Numerical modeling of the emplacement of Socompa rock avalanche, Chile . J Geophys Res 110 : B12202.1-12202.13 DOI:10.1029/2005JB003758

     

    VolcFlow also allows to reconstruct strain ellipse and surface déformation of the flows (See the movie file, 2.1 Mo).
    This may be very usefull to compare field structures of the natural deposits to numerical simulations.
    Read the following paper for further details:
    Kelfoun K, Druitt TH, van Wyk de Vries B, Guilbaud MN, Topographic reflexion of Socompa debris avalanche, Chile, Bull. Volcanol, 2008

    3.2 Simulation of pyroclastic flows

    The rheological behaviour of pyroclastic flows is very complex. VolcFlow can be used to estimate it, reproducing well known eruptions with different rheological laws and comparing numerical results to natural deposits.

     

    Pyroclastic flows at Tungurahua volcano (more details on Tungurahua activity)
    See the movie file (7 Mo)
    Read the following paper for further details: Kelfoun K, Samaniego P, Palacios P, Barba D, 2009, Is frictional behaviour suitable for pyroclastic flow simulation: comparison with a well constrained eruption at Tungurahua volcano (Ecuador). Bulletin of Volcanology.

    3.3 Hazard maps

    It is possible to generate hasard maps with VolcFlow. The maps can be drawn either for one event or for several scenarios taking into account a range of volumes, column heights, etc…
    Of course, this need the knowledge of the rheological behaviour of the simulated flows, which is the main problem to deal with.

     

    An example of Hasard map of Guagua Pinchincha, Ecuador.
    Hasard maps generated with VolcFlow at Guagua Pichincha (Ecuador) and Reventador (Ecuador, J. Bourquin)

     

    3.4 Erosion and sedimentation

    VolcFlow can also take into account sedimentation and erosion during emplacement.

    sediment

    Example of a viscous body sedimenting with time
    See the movie file (400 Ko)

    You can add you own laws of sedimentation and erosion in the “source”-string.
    For sedimentation, the mass and momentum conservation is simply achieved by changing the mass.
    In erosion, the flow is slowed down, and you have to write the laws needed for momentum conservation.

    eros

    Example of a viscous body sedimenting and eroding with time
    See the movie file (980 Ko)

     

  • 4.1 Pyroclastic flows and pyroclastic surges

    A modified version of  VolcFlow takes into account two “fluids”: a dense (e.g. block-and-ash flow) and a dilute (ash-cloud surge) fluids.
    It allows to simulate ash-cloud surge generated by the dense pyroclastic flows.

    Pyroclastic flows and ash-cloud surge at Merapi volcano

    Merapi_2010_sim2014_G


    4.2 Simulations of tsunami

    A modified version of  VolcFlow takes into account two “fluids”: rock avalanche and water. It allows to simulate tsunami generated
    by the entrance of a debris avalanche into the see or by coastal destabilization.

    tsunaweb

    Tsunami generated by a submarine destabilization at La Réunion
    See the movie file (12.5 Mo)
    Read the following paper for further details:
    Kelfoun K, Giachetti T, Labazuy Ph, Tsunamis hazard related to major catastrophic collapse at Reunion Island, Submitted J Geophys Res.

     

    Theoretical example of the debris avalanche entering a lake
    See the movie file (12.3 Mo)

    4.3 Fluidisation

    VolcFlow is able to advect the gas pressure and to change the frictions angles according to the pressure.

     

    fluidised

    Comparison between VolcFlow and laboratory experiments (Gueugneau V., Master 2 thesis)

    4.4 Cooling and lava flows

    mud flows                degasing flow

    A variation of the basic version allows advecting any properties. The rheology can depends on these properties.
    This allow to calculate the effect of cooling on lava flows and the effect of gaz diffusion on the rheology of granular flows.

    lava_web

     

     

     

  • These simple examples are done to learn how to use VolcFlow. The user must be able to write programs in Matlab before using VolcFlow.

     

    1. Dambreak

    dambreak

    2. Collapse

    A simple collapse on a topography
    defined by a function

    collapse

    3. Lava flow

    – how to model a source rate
    – use of a realistic topography
    saved in a mat-filelava

     4. Scripts

    – how to run a series of simulations?
    – probabilistic analysis
    – read a Surfer6 file for topography

     

     5. tsunami– how to use an image
    to define an initial perturbationtsunami

     

  • 6. Software

    6.1 Use of VolcFlow

    VolcFlow is writen with Matlab and is of very simple use. Just type VolcFlow in the command windows and the following figure appears.

    commandwindows  anim choice

    Choose the input file, check the result view with “representation” then click ok.
    The calculation runs showing the results at each representation time step.

    Pause, stop and restart

    It could be useful to pause VolcFlow if you need your computer to work with other softwares. Just clic on the “pause” button. To continue, press a key in the commande window.

    You can also stop VolcFlow during a calculation.
    First, you need to modifiy the inital input file by writing the name of the restart file : restart_file = ‘myrestart.dat’. Then, run VolcFlow as usually.
    Three possibilities allows to restart.

    1) VF_out.dat
    When you stop VolcFlow, a VF_out.dat file is automatically generated. The file contains the basic variables that allow VolcFlow to restart.
    It needs a small disk space but it cannot save user-defined variables. You have to rename this file before the next run if you want to conserve it.

    2) Workspace
    If you use your own variables, complex graphics, records of variables… the best way is to save the workspace of Matlab after VolcFlow stops.
    Clic on File and then on Save Workspace as. Then write in the input file : restart_file = ‘myrestart.mat’.
    VolcFlow will automatically detect the .mat extension, will load it and will restart exactly as if it was not interupted.
    The inconvenient is the large size of the mat-file on the disk.

    3) m-file 
    It is possible to call a external restart m-file. Write in the input file : restart_file = ‘myrestart.m’.
    The m-file must call a mat-file. It can be usefull if you need to change some variables of the input file.
    Indeed, if you choose to load a workspace, the modifications of the initial input-file (change of the duration of calculation, for example) will be lost.
    The structure of the restart m-file is first to load a workspace, then to change variables : tmax = 2000; for example.
    Be carreful with this option not to change variables that will cause VolcFlow to become unstable.

    6.2 Algorithm

    The following image summarizes the algorithm of VolcFlow. It may help the user to write the input file.

     

    VolcFlow can take into account frictional (with one or two friction angles), viscous, Bingham, Voellmy, etc…as well as user-defined behaviours.
    The default equation defining the stress in VolcFlow is :

     

    Where curb is the curbature of the topography in the flow direction.
    The terms in blue are to be defined in the input file.
    The internal friction (jint or delta_interne in the input file) is used to calculate Kactpass in the constitutive equation:

     

    6.3  Input file

    This section shows the input file that must be written to use VolcFlow.
    It simulate the flow a an initial mass released to the right and a mass brought at a constant rate to the left. (See the movie file (700 Ko) with a more complex representation).

     scriptexample example of two viscous flows:
    immediate release (right)
    and constant rate (left)

    Just keep the structure of this file and modify some lines to adapt the input file to the problem you want to solve.
    Calculation are always in 2D. To simulated 1D cases, as below, use 3 lines only and the boudary conditions written below.

    %This input file allows to simulate a 1D flow
    ncol=500;                   %number of rows
    nrow = 3;                   %number of lines
    dx_horiz = 0.004;           %x space step (m)
    dy_horiz = dx_horiz;        %y space step (m)
    dt=0.0005;                  %time step (if fixed by the user) in second
    tstep_adjust = 0;           %0 = fixed time step, 1 = variable time step defined by VolcFlow
    dtplot = 100*dt;            %time step of representation (s)
    tmax = 4;                   %time max of calculation (s)
    g=9.81;                     % gravity (m.s-2)
    delta_int = 0/180*pi;       %internal friction angle (rad)
    delta_bed   = 0/180*pi;     %external friction angle (rad)
    cohesion =      0;          %threshold (Pa)   
    rho = 1000;                 %density (kg.m-3)
    coef_u2 =   0;              %u2-resisting force (turbulence or collisional stress)
    viscosity = 1;              %viscosity (Pa.s)
    %representation  = 'cla; patch([x(1) x x(ncol)],[0 h(2,:)+z(2,:) 0],[0 h(2,:)*0 0],''Facecolor'',[0.5 0.8 1]);
    %hold on; patch([x(1) x x(ncol)],[0 z(2,:) 0],[0 h(2,:) 0],''Facecolor'',[0.7 0.7 0.3]); text(0.2,0.2,num2str(t)); axis equal; axis tight;';
    representation = 'cla; plot(x, z(2,:)+h(2,:)); hold on;plot(x, z(2,:), ''k''); axis equal '; %representation of results
    f_avi =  'c:\example.avi';     %used to produce a movie file during calculation
    f_data = 'c:\example.dat';     %used to store the data 
    source = 'if t<0.5; h(:,30:60)=h(:,30:60)+0.2*dt; end;';             %alimentation of the model
                       %be carreful: simple condition. Should take into account the momentum conservation
                       %Can also be used to add your own sedimentation laws.
    bound_cond = 'h2(1,:)=h2(2,:); h2(nrow,:)=h2(2,:);  ';    %Boudary conditions for 1D calculation
    x = [dx_horiz/2:dx_horiz:ncol*dx_horiz-dx_horiz/2];       %Definition of x and y axis. Not necessary.
    y = [dy_horiz/2:dy_horiz:nrow*dy_horiz-dy_horiz/2];
    z=ones(3,1)*( (x-1.2).^2/2+sin(x*10)/20)+0.2;     %Definition of the topography.
                                                      %It may be either a function or a DEM. z should be a nrow by ncol matrix
                                                               
    h(1:nrow, 1:ncol)=0;                              %Definition of the thickness, h should be a nrow by ncol matrix
    h(:, 450:480)  = 0.1; 
    % initial velocities, defined at the edges of the cells
    u_xx(1:nrow, 1:ncol-1)=0;
    u_xy(1:nrow, 1:ncol-1)=0;
    u_yy(1:nrow-1, 1:ncol)=0;
    u_yx(1:nrow-1, 1:ncol)=0;
    %other parameters that can be defined
    % indCy=[3 5 8];                      %cells were there is no flux. Numerical walls.
    % indCx=[12 53 62];
    % curvature = 0;                      %1 by default. 0 = the curvature of the topography is not taken into account
    % X_Rstress = ''; Y_Rstress = '';     %You can write your own resistive low that can depends on h, u, z ... for example a Pouliquen´s law.
    % CFLcond=0.5;                        %By default, the time step is automatically defined (if tstep_adjust == 1) according to the Courant-Friedrich-Levy criterion.
                                          %but it may be lowered to increase the stability. 1 = Courant-Friedrich-Levy criterion, 0.5 = two times lower.
    % restart_file = 'VF_out.dat';        %When VolcFlow stops, it generate a VF_out.dat file. It is possible to restart the calculation from the time step VolcFlow stops
                                          %using this line. You may change the name to avoid erasing of VF_out.dat at the next stop.
    % doubleUpwind = 0                    %0 by default. 1 = use of a second upwind scheme for momentum adevection. Sometimes more accurate but of a more difficult use.
    % uminstop=0;                         %If >0, VolcFlow will stop when the slowest velocity will be slide as a single mass. Usefull to simulate debris avalanches.                                   
    t=0; 

    6.4 Examples

    This section presents various examples to help understanding how to use VolcFlow.

    * Script

    The use of scripts is usefull to analyse the effect of one or several parameters on the simulation.
    The use is presented below:

    %First example: use of different input filesclose all
    clear all %the use of “clear all” can be necessary
    % as it is desactivated when using VolcFlow as a script
    %these 2 lines force VolcFlow to run as a script
    open volcflowfig.fig;set(findobj(‘tag’,’script’),’string’,0);autofilename=’cotopaxi1.m‘ %name of the 1st input file VolcFlow
    save(‘cotopaxi1.mat’, ‘h’); %save the final thickness onlyautofilename=’cotopaxi2.m’ %name of the 2nd input file
    VolcFlow
    save(‘cotopaxi2.mat’, ‘h‘); %save the final thickness only%and so on…
    %Second example: use of one input file and changing variablesclose all
    clear all %the use of “clear all” can be necessary
    % as it is desactivated when using VolcFlow as a script%these 2 lines force VolcFlow to run as a script
    open volcflowfig.fig;
    set(findobj(‘tag’,’script’),’string’,0);Volume=1e6; %this variable changes. The input file must take into account this variable.
    autofilename=’cotopaxi.m’
    VolcFlow
    save(‘coto´paxi1.mat’, ‘h’); %save the final thickness onlyVolume=1e7;
    autofilename=’cotopaxi.m’
    VolcFlow
    save(‘cotopaxi2.mat’, ‘h’); %save the final thickness only% and so on…

    This file simulate flows of various volumes. Each volume is defined by V in the script file (example_script.m).
    V is then used in the source file (source_cond.m) called by the input file (toposcript.m).
    At the end, all the areas covered by the flow are stacked to draw a kind of probabilistic hazard map.
    Uncompress, define the current directory and type example_script in the command window of Matlab.

    When using VolcFlow as a script, the “runs as a script” message appears at the right of the interface window. Below is the number of runs as a script.
    Close the interface before using VolcFlow in the normal way or write
    set(findobj(‘tag’,’script’),’string’,”) in the Matlab command window.
     

    * Source conditions

    1) how to calculate the momentum conservation at the source?

    Write source = ‘source_file;’ in the input file and put the in :

    % variation of thickness
    dh=h*0;
    dh(70:130, 10:50)=0.2*dt./S(70:130, 10:50);

    h=h+dh; %new thikness at the centers
    dhmx = (dh(:, 2:ncol) + dh(:,1:ncol-1)) / 2; %new thikness at x-edges
    dhmy = (dh(2:nrow, 🙂 + dh(1:nrow-1,:)) / 2; %new thikness at y-edges

    % momentum cinservation at the edges
    u_xx(dhmx>0) = (u_xx(dhmx>0).*hmx(dhmx>0) + 0)./(hmx(dhmx>0)+dhmx(dhmx>0));
    u_xy(dhmx>0) = (u_xy(dhmx>0).*hmx(dhmx>0) + 0)./(hmx(dhmx>0)+dhmx(dhmx>0));
    u_yx(dhmy>0) = (u_yx(dhmy>0).*hmy(dhmy>0) + 0)./(hmy(dhmy>0)+dhmy(dhmy>0));
    u_yy(dhmy>0) = (u_yy(dhmy>0).*hmy(dhmy>0) + 0)./(hmy(dhmy>0)+dhmy(dhmy>0));

    see also “a Bingham flow” in the Download section.

    2) how to define sedimentation and erosion laws?

    * “en masse” sliding

    If lA is defined (lA>0 in the input file), the mass is initially forced to slide in a coherent manner.
    1) The velocity of each cell, up, is calculated independently
    2) The mean velocity, ponderated by the thickness, is then calculated : um = S(up*h) / Sh
    3) Finally, the new velocity of each cell is calculated by its previous velocity and the mean velocity: un = up*(1-A) + um*A
    where A is defined by A = exp(-t / lA), t being the time.

    This allows a decrease of “coherency” with time, following an exponential law.

  • 7. Main variables used

    zchange               0 = slope calculation is done once, at the beginning
    1 = slope calculation is done at each time step. Use it if the topography changes with time

    indCx, indCy       indices of the cell borders in x and y where the velocity is forced to be null

    cohesion             cohesion for a Coulomb body or yield strength for a plastic flow (in Pa)

    delta_bed           basal friction angle for a Coulomb body

    delta_int             internal friction angle for a Coulomb body

    avant_flux          expression used to modify the parameters before the flux calculations

    bound_cond      expression used to define the boundary conditions

    ex : bound_cond = ‘h(:,1)=0; h(:,ncol)=0; h(1, :)=0; h(nrow, :)=0;’;

    under reconstruction

    CFLcond, chemin, coef_C, coef_u2, comptCFL, compteur2, coule, curvature, , dern_conn, doubleUpwind, dt, dtini, dtmax, dtmin, dtplot, dx_horiz, dy_horiz, erosion, f_avi, f_data, fichint, g, h, h_maxvel, hfluxmin, Hmxmin, icone, imageint, imageintR, , kk, lA, nbstepK, ncol, nomfich, nrow, p, pos_icone, pp, print_dt, pw, pz, qr, ratio_uxy, representation, restart_file, rho, Rstress_law, save_step, saved_var, securit, sedimentation, source, t, tmax, tstep_adjust, u, u_xx, u_xy, u_yx, u_yy, uminstop, VFstop, viscosity, vvf, X_Rstress, Y_Rstress, z

     

  •  8. Tests of VolcFlow

    8.1. Dambreak

    In order to check the accuracy of the numerical scheme of VolcFlow you can compare some numerical results with analytical solutions and with simulations based on other numerical schemes.

    The first figure shows comparisons between numerical and exact solutions of dam-break problems. The slope is horizontal and there is zero friction. This problem simulates the breakage of a dam separating an initial layer 1.5 m thick (left) from a layer 0.5 m thick (right). The solution reproduces almost exactly the analytical solution, and particularly the frontal shock wave and the thickness of the central plateau.

     fig3 fig5

    Test of  numerical solution against analog solution for a dambreak problem                               Symetry test of calcultions
    See the movie file (230 Ko)                                                                                                                See the movie file (750 Ko)

    8.2. Granular flow on a slope

    Since the numerical scheme of VolcFlow is based on a rectilinear coordinate system, it is also interesting to perform circular dambreak tests to ensure that the calculations are isotropic.
    In the above figure, a 6-m-diameter cylinder of zero-friction fluid, 1.5 m thick, is released onto a 0.5-m-thick, horizontal layer of the same fluid.
    The resulting degree of isotropy and shock resolution are both satisfactory, some small numerical oscillations disappearing progressively during the calculation.

     fig4

    Test of  numerical solution against analog solution for a dambreak problem on a slope

    Three comparisons with exact solutions obtained by Mangeney et al. (2000) for a dam-break problem on a slope with non-zero friction, and with zero thickness in front of the initial dam. The shape and velocity of the flow are accurately reproduced, even for the least favourable case of a steep slope and high friction angle. Note that the vertical exaggeration of the y-axis exaggerates the difference between numerical and analytical solutions.

         

    Sand flow (basal friction 32°) on an incline (34°) with a pyramidal obstacle (download the movie file, 2.5 Mo) 

    8.3. Viscosity

    The numerical scheme has been tested independently by Cordonnier et al., 2015.

    The benchmark shows a very good accuracy of the numerical scheme of VolcFlow for the simulation of viscous flows.

    see B. Cordonnier, E. Lev, and F. Garel, 2015, Benchmarking lava-flow models Geological Society, London, Special Publications, 426, first published on July 10, 2015, doi:10.1144/SP426.7

    cordonnier

    Known problems with VolcFlow

    1. a) You should use the version 2007b or more recent to be compatible withVolcFlow.
    2. b) You may receive the following message or wait more than one minute during the initialization phase:
                  Java exception occurred
           and […] org.apache.commons.net.ftp.FTP […]       solution:
             You should activate your Firewall – http://support.microsoft.com/kb/283673/fr  and allow Matlab to accès Internet.
      Without connection, you will be unable to use VolcFlow after 15 days.
    3. c) With some computers, 3D views cannot be captured in avi-files. This is due to an incompatibility between Matlab and the graphical capabilities of the computer used.
    4. d) VolcFlow works with Microsoft Windows only. I am trying to understand and solve the problème with Linux and McIntosh.

     

  • 9. Download

    vf_ianis_lr To obtain VolcFlow contact K. Kelfoun at k.kelfoun@opgc.fr
    VolcFlow is writen with Matlab and is of very simple use. Just type VolcFlow in the command windows and the following figure appears.

    Choose the input file, check the result view with “representation” then click ok.

    The calculation runs showing the results at each representation time step.

    (You must be able to write programs in Matlab before using VolcFlow. More than 200 people work with VolcFlow and I cannot help everybody. )

    Dat-reader file
    These files allow to read data from the .dat file generated by VolcFlow during calculation.
    You can modify the file to post-process your data.
    Saved variables are defined before the calculation in the input file using the following syntax: saved_var = {‘h’, ‘umx’, ‘umy’};
    Download the two files, put them in a same folder and write VF_data_reader in the command window of Matlab.

    VF_data_reader.m and the interface.

     

    This section is under construction

    Topography files
    Files are encoded in Surfer GS-binary Format.You can read them with Matalb using the following instructions :
    code = fscanf(fid,’%c’,4)
    ncol = fread(fid,1,’int16′)
    nlig = fread(fid,1,’int16′)
    xmin = fread(fid,1,’float64′)
    xmax = fread(fid,1,’float64′)
    ymin = fread(fid,1,’float64′)
    ymax = fread(fid,1,’float64′)
    zmin = fread(fid,1,’float64′)
    zmax = fread(fid,1,’float64′)
    z = fread(fid,’float32′);z = (reshape(z, ncol, nlig))’;

     

    Conversion vertical geometry / normal geometry 
    In VolcFlow 1.x.x and 3.x.x, the thickness is defined normal to the ground and not vertically (as in versions 2.x.x).
    For debris avalanches and dome collapses, it is often convenient to use DEM differences, which are defined vertically.

    This code allows to convert vertical thickness to normal thickness: vertical2normal.m
    You can use it in this input file.

    This code allows to convert normal thickness to vertical thickness: normal2vertical.m
    You can use it to visualize your results.

    Downloadable examples
    Just unzip, put VolcFlow.p and VolcFlowFig.fig in the same folder, define it in the path of Matlab and write “VolcFlow” in the Matlab command window.
    Select the input file (Socompa.m or lava.m) and click ok. VolcFlow needs to be connected to internet every two weeks to work.

    Socompa avalanche (low resolution) A Bingham flow (how to define source conditions with an image)

    Use these lines to calculate the center of mass of your flows or your deposits:

    [I,J]=meshgrid(1:ncol, 1:nrow);
    ic = sum(sum(h.*I))./sum(sum(h));
    jc = sum(sum(h.*J))./sum(sum(h));
    fprintf(‘The center of mass is located in i=%f, j=%f (in meshes).\n’, ic,jc);
    %plot(ic*dx_horiz, jc*dy_horiz, ‘*g’)

     

    !!! Because of the too large number of users (>200), the management of VolcFlow is no longer possible.

    VolcFlow is no longer distributed and cannot be downloaded !!!

 

 

 

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