Code repository for "Numerical Analysis of a Nonlinear Temperature Enhanced Diffusion Model for Drug Delivery"

This repository contais the code for "Numerical Analysis of a Nonlinear Temperature Enhanced Diffusion Model for Drug Delivery".

To run the code in this repository, first you should set up the prob1_env conda environment from environment.yml:

conda env create -f environment.yml
conda activate prob1_env

Core source files are in src/. Convergence studies are in Jupyter Notebook files in the root directory.

Intended use

Once the conda environment is set up, you can verify that all tests are passing by running:

pytest tests

Then, running the notebooks for reproducing the convergence studies is the next step. To run a notebook, it should be in project's root folder. Simply open the notebook and run all cells. The first cell will add src/ to the Python's system path.

Files Structure

Here is a brief description of the purpose of the files in src/:

• prob1base.py - Core logic, numerical method, discretization, etc.

• utils_for_testing.py - Utilities specifically for the test files in tests/.

• cvg_studies_base.py - Contains helper functions for programming the convergence studies. Not notebook specific. Can be used for regular scripts whose purpose is to perform convergence studies as well.

• mms_trial_utils.py - Main utilities for running a simulation against a manufactured solution.

• prob1_mms_cases.py - A library of manufactured solutions for studies.

• notebook_studies_helpers.py - Similar to cvg_studies_base.py, however these target utilities specifically helpful to notebook studies.

The following list is a description of the notebook files, and the convergence studies they cover. Some remarks are in order: "MMS" refers to "Method of Manufactured Solutions", "reghcstriple" refers to "regularized Heaviside applied to $c_s$ within its containing triple product". Not just that, the following descriptions might be cryptic without knowledge from the paper.

• MMSCaseNonFullySmoothPol_cpcsH2_TclcdH2_reghcstriple_convergence_study - For this study, we'll use the MMSCaseNonFullySmoothPol_cpcsH2_TclcdH2 MMS case: a solution which is just short regular enough on the $\mathbb P_1$ variables ($T, c_l, c_d$) for order 2 spatial convergence according to our results, while $\mathbb P_0$ variables ($c_p, c_s$) are just regular enough. More precisely, all $\mathbb P_0$ and $\mathbb P_1$ variables are in $H^2 \setminus H^3$. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial convergence breakdown.

• MMSCaseNonFullySmoothPol_cpcsH1_TclcdH2_reghcstriple_convergence_study - For this study, we'll use the MMSCaseNonFullySmoothPol_cpcsH1_TclcdH2 case: a solution which is just short of regular enough for order 2 spatial convergence. More precisely, $\mathbb P_0$ variables ($c_p, c_s$) are in $H^1 \setminus H^2$, and $\mathbb P_1$ variables ($T, c_l, c_d$) are in $H^2 \setminus H^3$. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial convergence breakdown.

• MMSCaseExpSin_reghcstriple_convergence_study - For this study, we'll use the MMSCaseExpSin case: smooth solution with sinusoidal behavior. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial and temporal convergence.

• MMSCaseNonFullySmoothPol_cpcsH2_TclcdH3_reghcstriple_convergence_study - For this study, we'll use the MMSCaseNonFullySmoothPol_cpcsH2_TclcdH3 case. This provides a solution which is just regular enough for order 2 spatial convergence according to your results. More specifically, $\mathbb P_1$ variables ($T, c_l, c_d$) are in $H^3 \setminus H^4$ and $\mathbb P_0$ variables ($c_p, c_s$) are in $H^2 \setminus H^3$. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial and temporal convergence.

• MMSCasePol_reghcstriple_convergence_study - For this study, we'll use the MMSCasePol case: a smooth solution with a polynomial spacial profile. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial and temporal convergence.

• MMSCaseSlowlyChangingPeaks_Fast1e1_reghcstriple_convergence_study - For this study, we'll use the MMSCaseSlowlyChangingPeaks_Fast1e1 case: a smooth solution designed to lead to larger errors. The objective is to better see the convergence happening. See `src/prob1_mms_cases.py' for a precise definition. This study expects order 2 spatial and temporal convergence.

Disclaimer

This repository contains the code used to generate results for the associated scientific work and is provided as-is for reproducibility and research purposes.

The code is distributed under the MIT license. See LICENSE.