A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics
We present MDIRK: a multifluid second-order diagonally implicit Runge–Kutta method to study momentum transfer between gas and an arbitrary number ( N ) of dust species. The method integrates the equations of hydrodynamics with an implicit–explicit scheme and solves the stiff source term in the momen...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal Supplement Series |
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| Online Access: | https://doi.org/10.3847/1538-4365/ad14f9 |
| _version_ | 1797310987925192704 |
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| author | Leonardo Krapp Juan Garrido-Deutelmoser Pablo Benítez-Llambay Kaitlin M. Kratter |
| author_facet | Leonardo Krapp Juan Garrido-Deutelmoser Pablo Benítez-Llambay Kaitlin M. Kratter |
| author_sort | Leonardo Krapp |
| collection | DOAJ |
| description | We present MDIRK: a multifluid second-order diagonally implicit Runge–Kutta method to study momentum transfer between gas and an arbitrary number ( N ) of dust species. The method integrates the equations of hydrodynamics with an implicit–explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge–Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with ${ \mathcal O }(N)$ operations, instead of standard matrix inversion, which is ${ \mathcal O }{(N)}^{3}$ . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas–dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods. |
| first_indexed | 2024-03-08T01:52:01Z |
| format | Article |
| id | doaj.art-75bd200db62345afa6bc2dbc419f720f |
| institution | Directory Open Access Journal |
| issn | 0067-0049 |
| language | English |
| last_indexed | 2024-03-08T01:52:01Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal Supplement Series |
| spelling | doaj.art-75bd200db62345afa6bc2dbc419f720f2024-02-14T09:40:53ZengIOP PublishingThe Astrophysical Journal Supplement Series0067-00492024-01-012711710.3847/1538-4365/ad14f9A Fast Second-order Solver for Stiff Multifluid Dust and Gas HydrodynamicsLeonardo Krapp0https://orcid.org/0000-0001-7671-9992Juan Garrido-Deutelmoser1https://orcid.org/0000-0002-7056-3226Pablo Benítez-Llambay2https://orcid.org/0000-0002-3728-3329Kaitlin M. Kratter3https://orcid.org/0000-0001-5253-1338Department of Astronomy and Steward Observatory, University of Arizona , Tucson, AZ 85721, USA ; krapp@arizona.eduInstituto de Astrofísica, Pontificia Universidad Católica de Chile , Av. Vicuña Mackenna 4860, 782-0436 Macul, Santiago, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez , Av. Diagonal las Torres 2640, Peñalolén, Chile; Data Observatory Foundation , ANID Technology Center No. DO210001, ChileDepartment of Astronomy and Steward Observatory, University of Arizona , Tucson, AZ 85721, USA ; krapp@arizona.eduWe present MDIRK: a multifluid second-order diagonally implicit Runge–Kutta method to study momentum transfer between gas and an arbitrary number ( N ) of dust species. The method integrates the equations of hydrodynamics with an implicit–explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge–Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with ${ \mathcal O }(N)$ operations, instead of standard matrix inversion, which is ${ \mathcal O }{(N)}^{3}$ . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas–dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.https://doi.org/10.3847/1538-4365/ad14f9Astrophysical dust processesPlanet formationComputational astronomy |
| spellingShingle | Leonardo Krapp Juan Garrido-Deutelmoser Pablo Benítez-Llambay Kaitlin M. Kratter A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics The Astrophysical Journal Supplement Series Astrophysical dust processes Planet formation Computational astronomy |
| title | A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics |
| title_full | A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics |
| title_fullStr | A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics |
| title_full_unstemmed | A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics |
| title_short | A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics |
| title_sort | fast second order solver for stiff multifluid dust and gas hydrodynamics |
| topic | Astrophysical dust processes Planet formation Computational astronomy |
| url | https://doi.org/10.3847/1538-4365/ad14f9 |
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