--- title: 'The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained' # The Pencil Code is used and developed by the 37 authors, who define the Pencil Code Collaboration. # About half of the currently 560 papers that acknowledge the code are by others who picked up the code, which has been public since 2001. tags: - Fortran90 - fluid dynamics - magnetohydrodynamics - Python - IDL - astrophysics - radiation - inertial particles - combustion authors: - name: The Pencil Code Collaboration affiliation: 1 - name: Axel Brandenburg affiliation: "1, 2, 3" orcid: 0000-0002-7304-021X - name: Anders Johansen affiliation: 4 orcid: 0000-0002-5893-6165 - name: Philippe A. Bourdin affiliation: "5, 6" orcid: 0000-0002-6793-601X - name: Wolfgang Dobler affiliation: 7 - name: Wladimir Lyra affiliation: 8 orcid: 0000-0002-3768-7542 - name: Matthias Rheinhardt affiliation: 9 - name: Sven Bingert affiliation: 10 orcid: 0000-0001-9547-1582 - name: Nils Erland L. Haugen affiliation: "11, 12, 1" orcid: 0000-0002-9184-8722 - name: Antony Mee affiliation: 13 - name: Frederick Gent affiliation: "9, 14" orcid: 0000-0002-1331-2260 - name: Natalia Babkovskaia affiliation: 15 - name: Chao-Chin Yang affiliation: 16 orcid: 0000-0003-2589-5034 - name: Tobias Heinemann affiliation: 17 orcid: 0000-0002-2476-9733 - name: Boris Dintrans affiliation: 18 - name: Dhrubaditya Mitra affiliation: 1 orcid: 0000-0003-4861-8152 - name: Simon Candelaresi affiliation: 19 orcid: 0000-0002-7666-8504 - name: Jörn Warnecke affiliation: 20 orcid: 0000-0002-9292-4600 - name: Petri J. Käpylä affiliation: 21 orcid: 0000-0001-9619-0053 - name: Andreas Schreiber affiliation: 15 - name: Piyali Chatterjee affiliation: 22 orcid: 0000-0002-0181-2495 - name: Maarit J. Käpylä affiliation: "9, 20" orcid: 0000-0002-9614-2200 - name: Xiang-Yu Li affiliation: 1 orcid: 0000-0002-5722-0018 - name: Jonas Krüger affiliation: "11, 12" orcid: 0000-0001-8036-0695 - name: Jørgen R. Aarnes affiliation: 12 orcid: 0000-0002-5899-2597 - name: Graeme R. Sarson affiliation: 14 orcid: 0000-0001-6774-9372 - name: Jeffrey S. Oishi affiliation: 23 orcid: 0000-0001-8531-6570 - name: Jennifer Schober affiliation: 24 orcid: 0000-0001-7888-6671 - name: Raphaël Plasson affiliation: 25 orcid: 0000-0003-2319-1463 - name: Christer Sandin affiliation: 1 orcid: 0000-0002-6370-5505 - name: Ewa Karchniwy affiliation: "12, 26" orcid: 0000-0001-6709-1160 - name: Luiz Felippe S. Rodrigues affiliation: "14, 27" orcid: 0000-0002-3860-0525 - name: Alexander Hubbard affiliation: 28 - name: Gustavo Guerrero affiliation: 29 orcid: 0000-0002-2671-8796 - name: Andrew Snodin affiliation: 14 - name: Illa R. Losada affiliation: 1 orcid: 0000-0002-0416-7516 - name: Johannes Pekkilä affiliation: 9 orcid: 0000-0002-1974-7150 - name: Chengeng Qian affiliation: 30 orcid: 0000-0002-5560-5475 affiliations: - name: Nordita, KTH Royal Institute of Technology and Stockholm University, Sweden index: 1 - name: Department of Astronomy, Stockholm University, Sweden index: 2 - name: McWilliams Center for Cosmology & Department of Physics, Carnegie Mellon University, PA, USA index: 3 - name: GLOBE Institute, University of Copenhagen, Denmark index: 4 - name: Space Research Institute, Graz, Austria index: 5 - name: Institute of Physics, University of Graz, Graz, Austria index: 6 - name: Bruker, Potsdam, Germany index: 7 - name: New Mexico State University, Department of Astronomy, Las Cruces, NM, USA index: 8 - name: Astroinformatics, Department of Computer Science, Aalto University, Finland index: 9 - name: Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen, Germany index: 10 - name: SINTEF Energy Research, Trondheim, Norway index: 11 - name: Norwegian University of Science and Technology, Norway index: 12 - name: Bank of America Merrill Lynch, London, UK index: 13 - name: School of Mathematics, Statistics and Physics, Newcastle University, UK index: 14 - name: No current affiliation index: 15 - name: University of Nevada, Las Vegas, USA index: 16 - name: Niels Bohr International Academy, Denmark index: 17 - name: CINES, Montpellier, France index: 18 - name: School of Mathematics and Statistics, University of Glasgow, UK index: 19 - name: Max Planck Institute for Solar System Research, Germany index: 20 - name: Institute for Astrophysics, University of Göttinge, Germany index: 21 - name: Indian Institute of Astrophysics, Bengaluru, India index: 22 - name: Department of Physics & Astronomy, Bates College, ME, USA index: 23 - name: Laboratoire d'Astrophysique, EPFL, Sauverny, Switzerland index: 24 - name: Avignon Université, France index: 25 - name: Institute of Thermal Technology, Silesian University of Technology, Poland index: 26 - name: Radboud University, Netherlands index: 27 - name: Department of Astrophysics, American Museum of Natural History, NY, USA index: 28 - name: Physics Department, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil index: 29 - name: State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, China index: 30 date: 17 September 2020 bibliography: paper.bib --- # Summary The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) [@2010ascl.soft10060B] to meteorological cloud microphysics [@2017JAMES.9.1116L] and engineering applications in combustion [@2011JCoPh.230.1B]. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid. A related module has also been adapted to perform ray tracing and to solve the eikonal equation. The code is being used for Cartesian, cylindrical, and spherical geometries, but further extensions are possible. One can choose between different time stepping schemes and different spatial derivative operators. High-order first and second derivatives are used to deal with weakly compressible turbulent flows. There are also different diffusion operators to allow for both direct numerical simulations (DNS) and various types of large-eddy simulations (LES). # High-level functionality An idea about the range of available modules can be obtained by inspecting the examples under pencil-code/samples/. Those are low resolution versions related to applications published in the literature. Some of the run directories of actual production runs are published through Zenodo. Below a list of method papers that describe the various applications and tests: * Coagulation and condensation in turbulence [@2008A&A.486.597J; @2017JAMES.9.1116L], * Radiative transfer [@2006A&A.448.731H; @2014A&A.571A.68B; @2020GApFD.114.162B], * Chiral magnetic effect in relativistic plasmas [@2018ApJ.858.124S], * Primordial gravitational waves [@2020GApFD.114.130R], * Modeling homochirality at the origin of life [@2004IJAsB.3.209B; @2019OLEB.49.49B], * Modeling of patterned photochemical systems [@2012ChemEurJ], * Gaseous combustion and detonation [@2011JCoPh.230.1B; @Zhang_etal_2020comb; @2017CNF.185a160], * Burning particles, resolved or unresolved [@2020GApFD.114.58Q], * Flows around immersed solid objects [@2019IJCFD.33.43A; @2020GApFD.114.35A; @2010JFM.661a239], * Test-field method for turbulent MHD transport [@2010A&A.520A.28R; @2010PhST.142a4028B; @2018A&A.609A.51W], * Mean-field MHD [@2013SoPh.287.293K; @2013A&A.556A.106J], * Spherical shell dynamos and convection [@2009ApJ.697.923M; @2020GApFD.114.8K], * Boris correction for coronal physics [@2020GApFD.114.213C], * Thermal instability and mixing [@2012ApJ.758.48Y], * Implicit solver for temperature [@2008A&A.484.29G], * Dust-gas dynamics with mutual drag interaction [@2007ApJ.662.613Y; @2016ApJS.224.39Y], * Boundary conditions for the solar atmosphere and HDF5 format [@2020GApFD.114.235B]. # Statement of need and purpose of software The code is an easily adaptable tool for solving both standard MHD equations as well as others, such as the test-field equations. Significant amounts of runtime diagnostics as well as Python and IDL libraries for post-processing are available. Among the currently 83 developers with check-in permission, there are currently 18 owners who can give others check-in permission. Of the developers, 35 have done more than 35 commits. Users have access to the latest development version and can ask to join the circle of developers by contacting one of the owners. Every revision on GitHub is verified on 9 tests on travis-ci.com. The current version is also automatically being tested on 59 hourly tests and on 79 daily tests. Continuous progress on the code is driven by the research of individual developers. Further developments and interactions between developers and users are being promoted through annual user meetings since 2004 and a newsletters since 2020. Since 2016, a steering committee of five elected owners reviews the progress and can take decisions of general concern to the Pencil Code community. # Ongoing research using the Pencil Code Current research includes topics from stellar physics, interstellar and intercluster medium, the early universe, as well as from meteorology and engineering: small-scale dynamos and reconnection; primordial magnetic fields and decaying turbulence; gravitational waves from turbulent sources; planet formation and inertial particles; accretion discs and shear flows; coronal heating and coronal mass ejections; helical dynamos, helical turbulence, and catastrophic quenching; helioseismology; strongly stratified MHD turbulence and negative effective magnetic pressure instability; convection in Cartesian domains; global convection and dynamo simulations; turbulent transport and test-field methods; hydrodynamic and MHD instabilities and turbulence; chiral MHD; turbulent gaseous and solid combustion, particle clustering and deposition on solid walls, front propagation, radiation & ionization. As of July 2020, 564 papers have been published that acknowledge use of the Pencil Code [@zenodo.3466444]. # Key references The Pencil Code is unique in two ways: the high level of flexibility and modularity, and the way it is organized (open source, distributed ownership, openness of development version). Other software addressing related needs include: Athena, CO5BOLD, ENZO, MuRAM, NIRVANA, Stagger, ZEUS, Snoopy, and several other LES codes. There are also several other engineering DNS codes such as Sandia-3-Dimensional (S3D), a high-order compressible code, optimized for combustion, which is not open source, however. Another example is SpECTRE, a task-based discontinuous Galerkin code for relativistic astrophysics [@Kidder_2017]. In addition, there are frameworks like Dedalus or Cactus, which allow one to program the equations in symbolic form. Some recent research areas that made use of the Pencil Code, as evidenced by the aforementioned document listing all those papers [@zenodo.3466444], include: * Flows around immersed solid objects [@2010JFM.661a239], * Particle clustering in supersonic and subsonic turbulence [@2019MNRAS.483.5623M; @Karchniwy_etal_2019], * Cloud microphysics [@2017JAMES.9.1116L], * Planet and planetesimal formation [@2007Natur.448.1022J; @2007ApJ.670.805O; @2009A&A.497.869L], * Global simulations of debris disks [@2013Natur.499.184L], * Stratified shearing box simulations, also with dust [@2011ApJ.740.18O; @2018ApJ.861.47S; @2018ApJ.868.27Y], * Supernova-driven turbulence [@2013MNRAS.432.1396G], * Solar dynamo and sunspots [@2005ApJ.625.539B; @2007ApJ.669.1390H], * Solar corona above active regions [@2011A&A.530A.112B; @2013A&A.555A.123B; @2016PhRvL.116j1101C], * Fully convective star in a box [@2006ApJ.638.336D], * Dynamo wave in spherical shell convection [@2012ApJ.755L.22K; @2014ApJ.796L.12W], * Convection with Kramers opacity law [@2017ApJ.845.23K; @2019A&A.631.122K; @2020GApFD.114.8K], * MHD turbulence and cascades [@2004PhRvE.70a6308H], * Turbulent diffusivity quenching with test fields [@2008ApJ.676.740B; @2014ApJ.795.16K]. # Acknowledgements We acknowledge contributions from all submitters and their supporting funding agencies. In particular, we mention the ERC Advanced Grant on Astrophysical Dynamos (No 227952), the Swedish Research Council, grants 2012-5797, 2013-03992, 2017-03865, and 2019-04234, the National Science Foundation under the grant AAG-1615100, the FRINATEK grant 231444 under the Research Council of Norway, SeRC, the grant "Bottlenecks for particle growth in turbulent aerosols" from the Knut and Alice Wallenberg Foundation, Dnr.\ KAW 2014.0048, the ReSoLVE Centre of Excellence (grant number 307411), the research project ‘Gaspro’, financed by the Research Council of Norway (267916), the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Project UniSDyn, grant agreement n:o 818665), and the Deutsche Forschungsgemeinschaft (DFG) Heisenberg programme grant KA 4825/2-1. # References