Grain growth for astrophysics with Discontinuous Galerkin schemes

by Maxime Lombart and Guillaume Laibe

Manuscript is submitted for publication in the Monthly Notices of the Royal Astronomical Society.

This repository contains the data and code used to reproduce all figures shown in the paper.

Abstract

Depending on their sizes, dust grains store more or less charges, catalyse more or less chemi- cal reactions, intercept more or less photons and stick more or less efficiently to form embryos of planets. Hence the need for an accurate treatment of dust coagulation and fragmentation in numerical modelling. However, existing algorithms for solving the coagulation equation are over-diffusive in the conditions of 3D simulations. We address this challenge by developping a high-order solver based on the Discontinuous Galerkin method. This algorithm conserves mass to machine precision and allows to compute accurately the growth of dust grains over several orders of magnitude in size with a very limited number of dust bins.

Results

Python 3 is used to produce figures for constant, additive and multiplicative coagulation kernels.

Benchmarks

Constant kernel

Python scripts are located in kconst/code.

Positivity, mass conservation and accuracy

Data are located in kconst/data/simu.

The corresponding script is plot_kconst_simu.py.

The corresponding scripts are plot_kconst_xmean_xmeanlog.py and plot_kconst_error_moments.py.

Stability in time

Data are located in kconst/data/simu. The corresponding script is plot_kconst_errors_simu.py.

Convergence analysis

Data are located in kconst/data/EOC. The corresponding script is plot_kconst_convergence.py.

Computational efficiency

Data are located in kconst/data/perf with the files perf.txt. The time for DG is "time ODE perf" and for DGGQ is "time perf". The corresponding script is plot_kconst_DG_DGGQ_perf.py.

Improvement by a factor ~ 4 in computational time.

Additive kernel

Positivity, mass conservation and accuracy

Data are located in kadd/data/simu.

The corresponding script is plot_kadd_simu.py.

The corresponding scripts are plot_kadd_xmean_xmeanlog.py and plot_kadd_error_moments.py.

Stability in time

Data are located in kadd/data/simu. The corresponding script is plot_kadd_errors_simu.py.

Convergence analysis

Data are located in kadd/data/EOC. The corresponding script is plot_kadd_convergence.py.

Computational efficiency

Data are located in kadd/data/perf with the files perf.txt. The time for DG is "time ODE perf" and for DGGQ is "time perf". The corresponding script is plot_kadd_DG_DGGQ_perf.py.

Improvement by a factor ~ 2000 in computational time.

Multiplicative kernel

Positivity, mass conservation and accuracy

Data are located in kmul/data/simu.

The corresponding script is plot_kmul_simu.py.

The corresponding script is plot_kmul_xmean_xmeanlog.py.

The corresponding script is plot_kmul_error_moments.py.

Stability in time

Data are located in kmul/data/simu. The corresponding script is plot_kmul_errors_simu.py.

Convergence analysis

Data are located in kmul/data/EOC. The corresponding script is plot_kmul_convergence.py.

Computational efficiency

Data are located in kmul/data/perf with the files perf.txt. The time for DG is "time ODE perf" and for DGGQ is "time perf". The corresponding script is plot_kmul_DG_DGGQ_perf.py.

Improvement by a factor ~ 8 in computational time.