README

This repository contains a small example that demonstrates how use the hydrofrac module in FDMAP. The hydrofrac module couples a nominally planar fluid-filled crack to a surrounding elastic solid.

Install FDMAP

To run this example, you need to obtain the source code for FDMAP, available here. To learn more about FDMAP, see the user guide. As stated in the user guide, you need a Fortran compiler, MPI, and suitable implementation of the BLAS and LAPACK libraries installed.

Docker image (optional)

To simplify the installation, this repository contains a Docker file that you can use to run FDMAP inside a docker container. To build the docker image, clone this repository and type

$ docker build .

If all goes well, all of the necessary dependencies should be installed and fdmap should be compiled. The final step of the build process also runs a simulation. You can find the compiled version of FDMAP inside the directory fdmap within the docker container, as well as simulation data in simulation. To view any of the data, you can interact with the newly created docker image by first looking up its name

$ docker images

Copy the IMAGE ID e.g., 1a118489e5e4 and run

$ docker run -it docker run -it 1a118489e5e4 /bin/bash
Run the simulation using the provided example input file (see below),

```bash
$ root@4061eb40b079:/# cd simulation && ./fdmap hydrofrac.in

List generated simulation data:

$ root@4061eb40b079:/# ls simulation
curves          hydrofrac.m          hydrofrac_B_sxy.t    hydrofrac_B_vx.t    hydrofrac_B_x.t    hydrofrac_I_p.t    hydrofrac_I_v.t     hydrofrac_I_wp.t   hydrofrac_I_y.t
fdmap           hydrofrac_B_sxx.dat  hydrofrac_B_syy.dat  hydrofrac_B_vy.dat  hydrofrac_B_y.dat  hydrofrac_I_u.dat  hydrofrac_I_wm.dat  hydrofrac_I_x.dat  hydrofrac_demo.in
hydrofrac.ckpt  hydrofrac_B_sxx.t    hydrofrac_B_syy.t    hydrofrac_B_vy.t    hydrofrac_B_y.t    hydrofrac_I_u.t    hydrofrac_I_wm.t    hydrofrac_I_x.t    
hydrofrac.in    hydrofrac_B_sxy.dat  hydrofrac_B_vx.dat   hydrofrac_B_x.dat   hydrofrac_I_p.dat  hydrofrac_I_v.dat  hydrofrac_I_wp.dat  hydrofrac_I_y.dat

To copy simulation data from the container to the host, you need the CONTAINER ID. Here's how to get the last used container ID.

$ docker ps -alq
$ abf4605d89e7

Then you can copy the simulation directory from the container to the host via

 $ mkdir -p simulation
 $ docker cp abf4605d89e7:/simulation simulation

Input file

The fluid-filled crack acts as an interface between two elastic blocks, and it has a few options that you can configure.

&hydrofrac_list
coupled = T,
! Use a linear model in the width-averaged approximation. 
linearized_walls = T,
! Use implicit-explicit time stepping to prevent prohibitely expensive small time steps (first order
in time accuracy)
operator_splitting = T,
! Enable fluid viscocity
inviscid = F,
! Numerical method to use 
FDmethod = 'SBP6',
! Number of grid points inside the fracture (along the width direction)
n = 40,
! Nominal wall opening 
w0 = 1.000000d-03,
! Fluid density
rho0 = 1.000000d+00,
! Fluid bulk modulus
K0 = 2.250000d+06,
! Fluid dynamic viscosity
mu = 1.000000d-06,
! Put a source term inside the crack at (0,0)
source_term = T,
xsource = 0.000000d+00,
ysource = 0.000000d+00,
Asource = 1.000000d+06,
wsource = 8.000000d-01,
tsource = 1.000000d-03,
! Apply left pressure boundary condition with sine-wave boundary data
! see hydrofrac.f90 for details
bcL = 'sin_p', 
bcLomega = 6.283185d+02,
bcRA = 1.000000d-02,
bcRomega = 6.283185d+02,
! Store LU factorization of diffusion operator as a banded matrix 
banded_storage = T

More details regarding the hydrofrac options are documented in the source code itself, see fdmap/hydrofrac.f90.

Crack profiles and variable grid stretching along the width direction

The input file above configures a tabular crack with uniform grid spacing across the width of the crack. If you need to use a tapered profile and/or need to resolve boundary layers, you need to generate some data files and link to them in the input file. For example, add the following to the input file:

geom_file = 'profile.curve',
var_file = 'grid_stretching.var',

You can use the matlab functions found in matlab/write_hf_profile.m and matlab/write_hf_var.m to generate these files.

Postprocessing

The script, postprocess.m, loads the simulation data and generates a space time plot of the pressure field inside the crack. For this script to work, it needs to find the fdmap matlab files. If you put the fdmap directory next to the script, it should work. Otherwise, you need to modify the script postprocess.m accordingly.

Here is the expected output from running the postprocessing script.

The pressure field is is intentionally poorly resolved so that the simulation runs fast on a single CPU core.