This week I focused on establishing a benchmark for my simulations. As I mentioned in the previous blog post, I created a function that creates a parallel plate model for a given fracture aperture. This model serves as the benchmark for our simulation. My main job this week was to run the Lattice-Boltzmann simulation on this benchmark for an aperture of 5 voxel units and test the result with the analytical solution. The LB simulation is supposed to yield a velocity map of fluid through the fracture. I'll attach a visualization of what this looks like below, created in Paraview. Lonestar (the supercomputer I am utilizing for the LB simulation) creates a vti file which I can open in Paraview.
The analytical solution is a formula that describes the velocity using aperture, width of fracture and pressure differential between the front and rear of the fracture. I created a function in MatLab that plots the analytical solution. After this I dissected the velocity map in Paraview. I analyzed the velocities along a line draw between the "walls" of the fracture for the first "slice (beginning)" of the fracture. Ideally the results should be exactly- or almost exactly the same. My results for the simulation were different than the the analytical solution. I believe this might be due to the inputs I used to create the benchmark lattice. I'm rerunning the simulation using a new lattice file. I'll be comparing the velocities at the beginning, middle and end slice of the fracture. It shouldn't be too bad.
The analytical solution is a formula that describes the velocity using aperture, width of fracture and pressure differential between the front and rear of the fracture. I created a function in MatLab that plots the analytical solution. After this I dissected the velocity map in Paraview. I analyzed the velocities along a line draw between the "walls" of the fracture for the first "slice (beginning)" of the fracture. Ideally the results should be exactly- or almost exactly the same. My results for the simulation were different than the the analytical solution. I believe this might be due to the inputs I used to create the benchmark lattice. I'm rerunning the simulation using a new lattice file. I'll be comparing the velocities at the beginning, middle and end slice of the fracture. It shouldn't be too bad.