Introduction and verification of FEDM, an open-source FEniCS-based discharge modelling code - datasetThe dataset contains the data presented in the paper introducing the FEDM (Finite Element Discharge Modelling) code. The FEDM code was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method to solve partial differential equations. It extends FEniCS with features that allow the automated implementation and numerical solution of fully-coupled fluid-Poisson models, including an arbitrary number of particle balance equations. The code is verified using the method of exact solutions and benchmarking. The physically based examples of a time-of-flight experiment, a positive streamer discharge in atmospheric-pressure air and a low-pressure glow discharge in argon are used as rigorous test cases for the developed modelling code and to illustrate its capabilities. The performance of the code is compared to the commercial software package COMSOL Multiphysics®, and a comparable parallel speed-up is obtained. It is shown that the iterative solver implemented by FEDM performs particularly well on high-performance compute clusters.

]]>FEniCSfinite element methodglow dischargestreamer dischargetime-of-flight experimentPlasma Chemical Processes694222be-81e7-4ea8-ad7d-61fd528156942023-04-04T00:28:52+02:002023-04-03T23:42:21+02:00enINPIntroduction and verification of FEDM-Fig.4Temporal evolution of the electron number density profile at the symmetry axis in time-of-flight experiment. The simulations started at t_0 = 2 ns and were carried out with the constant time step size ∆t = 1 ps using a mesh consisting of 100 000 elements. The data are given in a form of a table where a first column is axial coordinate z, the second column is analytic solution for the t = 2 ns, and each subsequent columns are analytic and numeric solutions for different time steps in range from 2.5 to 4 ns.

Dataset: 'Figure4'
column 1: z [m]
column 2: n_e [m^-3] analytic t = 2 ns
column 3: n_e [m^-3] analytic t = 2.5 ns
column 4: n_e [m^-3] numeric t = 2.5 ns
column 5: n_e [m^-3] analytic t = 3 ns
column 6: n_e [m^-3] numeric t = 3 ns
column 7: n_e [m^-3] analytic t = 3.5 ns
column 8: n_e [m^-3] numeric t = 3.5 ns
column 9: n_e [m^-3] analytic t = 4 ns
column 10: n_e [m^-3] numeric t = 4 ns

]]>2023-03-28T13:36:06+02:002023-04-03T23:31:04+02:00text/csvcsv108095https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-0Introduction and verification of FEDM-Fig.5Error of the numerical solution in L2 norm in dependence on the element size h for the time t = 3 ns and time step size ∆t = 0.02 ps. The first column represents element size h, i.e. circumradius of the triangle element, in [m], and the second one is the L2 error norm.

Dataset: 'Figure5'
column 1: h [m]
column 2: L2 error norm

]]>2023-03-28T13:55:51+02:002023-04-03T23:31:04+02:00text/csvcsv386https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-1Introduction and verification of FEDM-Fig.6(a)The file contains temporal evolution of the spatial profiles of the number density of electrons simulated up to 14 ns applying the FEDM code for the streamer benchmark case. The data are stored as a three-column form table where the first column is r [m], the second one z [m] and each subsequent number density of electrons in [m^-3] at different times during the streamer propagation (2, 6, 10 and 14 ns).

Dataset 'Figure 6a'
column 1: r [m]
column 2: z [m]
column 3: n_e [m^-3] @ t = 2 ns
column 4: n_e [m^-3] @ t = 6 ns
column 5: n_e [m^-3] @ t = 10 ns
column 6: n_e [m^-3] @ t = 14 ns

]]>2023-03-28T14:02:54+02:002023-04-03T23:31:04+02:00text/csvcsv58882188https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-2Introduction and verification of FEDM-Fig.6(b)Temporal evolution of the spatial profiles of the electric field simulated up to 14 ns applying the FEDM code for the streamer benchmark case. The data are stored as a three-column form table where the first column is r [m], the second one z [m] and subsequent ones magnitude of the electric field in [MV/m] at different times during the streamer propagation (2, 6, 10 and 14 ns).

Dataset 'Figure 6b'
column 1: r [m]
column 2: z [m]
column 3: |E| [MV/m] @ t = 2 ns
column 4: |E| [MV/m] @ t = 6 ns
column 5: |E| [MV/m] @ t = 10 ns
column 6: |E| [MV/m] @ t = 14 ns

]]>2023-03-28T14:07:35+02:002023-04-03T23:31:04+02:00text/csvcsv71502292https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-3Introduction and verification of FEDM-Fig.7(a)The electron number density profiles along the symmetry axis in the time range between 2 and 14 ns calculated using the FEDM code. The data are stored as in form of a table where the first column is z [m] and each subsequent number density of electrons in [m^-3] at different times during the streamer propagation (2, 4, 6, 8, 10, 12, and14 ns).

Dataset 'Figure 7a'
column 1: z [m]
column 2: n_e [m^-3] @ t = 2 ns
column 3: n_e [m^-3] @ t = 4 ns
column 4: n_e [m^-3] @ t = 6 ns
column 5: n_e [m^-3] @ t = 8 ns
column 6: n_e [m^-3] @ t = 10 ns
column 7: n_e [m^-3] @ t = 12 ns
column 8: n_e [m^-3] @ t = 14 ns

]]>2023-03-28T15:34:17+02:002023-04-03T23:31:04+02:00text/csvcsv136316https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-4Introduction and verification of FEDM-Fig.7(b)The electric field profiles along the symmetry axis in the time range between 2 and 14 ns calculated using the FEDM code. The data are stored in a table where the first column z [m] and subsequent ones the magnitude of the electric field in [MV/m] at different times during the streamer propagation (2, 4, 6, 8, 10, 12 and 14 ns).

Dataset 'Figure 7b'
column 1: z [m]
column 2: |E| [MV/m] @ t = 2 ns
column 3: |E| [MV/m] @ t = 4 ns
column 4: |E| [MV/m] @ t = 6 ns
column 5: |E| [MV/m] @ t = 8 ns
column 6: |E| [MV/m] @ t = 10 ns
column 7: |E| [MV/m] @ t = 12 ns
column 8: |E| [MV/m] @ t = 14 ns

]]>2023-03-28T15:35:35+02:002023-04-03T23:31:04+02:00text/csvcsv63691https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-5Introduction and verification of FEDM-Fig.8The data contain the streamer length in [cm] and streamer length with subtracted drift velocity multiplied by time in [cm] as a function of time calculated using the FEDM code. Note that in addition to present data, the data by CWI, DE and CN group are shown in the manuscript. The values were taken from a supplementary data provided with Bagheri B et al 2018 Plasma Sources Sci. Technol. 27 095002 article.

Dataset: 'Figure8'
column 1: t [ns]
column 2: L in [cm]
column 3: L-v_d*t in [cm]

]]>2023-03-28T15:37:54+02:002023-04-03T23:31:04+02:00text/csvcsv265https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-6Introduction and verification of FEDM-Fig.9The file contains the FEDM code simulation results of the spatiotemporal evolution of electron and ion density for the case of an abnormal glow discharge in argon at low-pressure. Due to their size, the data are saved as binary hdf5 file. The file can be opened using any program that supports opening hdf5 files, such as HDF Viewer, Origin Pro, Matlab, or various libraries in python. The data are stored as a set of 2D numpy arrays containing the mesh grid (with time t and axial coordinate z) and spatiotemporal distributions of electrons and ions. The number density along the axis is stored in each column for the given time over the rows.

Dataset: 'Figure9'
Size: 70800
Structured 2Darray 1: 'mesh_grid' H5T_IEEE_F64LE (double)
Structured 2Darray 2: 'Ar_plus' H5T_IEEE_F64LE (double)
Structured 2Darray 3: 'electrons' H5T_IEEE_F64LE (double)

]]>2023-03-28T15:40:18+02:002023-04-03T23:31:04+02:00application/octet-streamdata568448https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-7Introduction and verification of FEDM-Fig.10The file contains the axial density profiles of electrons, ions and the excited argon states at different times during ignition of the abnormal glow discharge in argon calculated using the FEDM code and COMSOL Multiphysics®. The data are given in a form of table whose structure is described below.

Dataset: 'Figure10'
column 1: z [m]
column 2: [e] [m^-3] t = 5e-6 s FEDM
column 3: [Ar^+] [m^-3] t = 5e-6 s FEDM
column 4: [Ar^] [m^-3] t = 5e-6 s FEDM
column 5: [e] [m^-3] t = 1e-5 s FEDM
column 6: [Ar^+] [m^-3] t = 1e-5 s FEDM
column 7: [Ar^] [m^-3] t = 1e-5 s FEDM
column 8: [e] [m^-3] t = 5e-5 s FEDM
column 9: [Ar^+] [m^-3] t = 5e-5 s FEDM
column 10: [Ar^] [m^-3] t = 5e-5 s FEDM
column 11: z [m] COMSOL
column 12: [e] [m^-3] @ t = 5e-6 s COMSOL
column 13: [Ar^+] [m^-3] @ t = 5e-6 s COMSOL
column 14: [Ar^] [m^-3] @ t = 5e-6 s COMSOL
column 15: [e] [m^-3] @ t = 1e-5 s COMSOL
column 16: [Ar^+] [m^-3] @ t = 1e-5 s COMSOL
column 17: [Ar^] [m^-3] @ t = 1e-5 s COMSOL
column 18: [e] [m^-3] @ t = 5e-5 s COMSOL
column 19: [Ar^+] [m^-3] @ t = 5e-5 s COMSOL
column 20: [Ar^] [m^-3] @ t = 5e-5 s COMSOL

]]>2023-03-28T16:01:01+02:002023-04-03T23:31:04+02:00text/csvcsv164213https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-8Introduction and verification of FEDM-Fig.11The data present the speed-up factors for the FEDM code and the commercial software package COMSOL Multiphysics® obtained for the streamer benchmark case. Note that simulations were performed for the early phase, until 500 ps. Note that the Newton-based nonlinear solver was used for the calculations in both cases. For the best overall performance, FEDM uses MUMPS, and COMSOL uses Pardiso as the direct solver. The data are presented in a table, where the first column is the number of physical cores, the second column is the speed-up of FEDM, and the third one is the speed-up of COMSOL.

]]>2023-03-28T16:03:33+02:002023-04-03T23:31:04+02:00text/csvcsv202https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-9Introduction and verification of FEDM-Fig.12The data contain the results of the performance test of the FEDM code obtained on two nodes with 32 physical cores, comparing direct and iterative linear solvers. The data are presented in a table. The first column is the number of physical cores, the second column is the speed-up obtained using a direct linear solver, and the third column contains the speed-up when the iterative solver was used.

]]>2023-03-28T16:04:42+02:002023-04-03T23:31:04+02:00text/csvcsv399https://gitlab.inptdat.de/dataset/introduction-and-verification-fedm-open-source-fenics-based-discharge-modelling-code-10DKANhttps://gitlab.inptdat.de