Numerical Solvers

I have developed various programs for generating numerical solutions to partial differential equations (PDEs), utilizing various programming languages such as C++, Matlab, FORTRAN, and Python. During my masters, my primary focus was on employing smoothness-enhancing accuracy-conserving (SIAC) filters for smoothing data obtained from spectral methods.

In recent years, I have developed clotFoam, an open-source general framework for simulating platelet-mediated coagulation. The solver is written in C++ and utilizes the open-source libraries of OpenFOAM version 9. For additional examples of codes that I have developed over the years, please visit my GitHub page.

Codes Available for Download at GitHub

Tutorial for clotFoam

clotFoam tutorial

Hemostasis in a Microfluidic Device

Using the clotFoam software, we are able to simulate platelet-mediated coagulation in a variety of geometries. This is an example of hemostasis in an extravascular injury that is modeled using an in-vitro microfluidic device. Blood enters the right channel while a buffer fluid enters the left channel at a lower flow rate. The difference in flow rates cause blood to flow through the horizontal channel which is coated with tissue factor and collagen proteins to initiate platelet adhesion and coagulation respectively.

Relevant publications: https://doi.org/10.1016/j.softx.2023.101483

GitHub project: https://github.com/d-montgomery/clotFoam/tree/main/tutorials/Hjunction3D

Thrombosis

In this example, we use the clotFoam software to simulate thrombosis from an intravascular injury.

Relevant publications: https://doi.org/10.1016/j.softx.2023.101483

GitHub project: https://github.com/d-montgomery/clotFoam/tree/main/tutorials/rectangle2D

Buoyancy Driven Convection

Simulating buoyancy driven convection in Matlab using a projection method to solve the Navier-Stokes equations with a Boussinesq approximation.

GitHub project: https://github.com/d-montgomery/buoyancyDrivenConvectionMatlab

SIAC Filtering

Employing smoothness increasing accuracy conserving (SIAC) filters to smooth approximations to the solutions to PDE's obtained from spectral methods in Matlab.

GitHub Project: https://github.com/d-montgomery/linearAdvectionSIACFiltering

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