A Fast second-order solver for stiff multifluid dust and gas hydrodynamics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909119552684032 |
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| author | Krapp, Leonardo Garrido-Deutelmoser, Juan Benítez-Llambay, Pablo Kratter, Kaitlin M. |
| author_facet | Krapp, Leonardo Garrido-Deutelmoser, Juan Benítez-Llambay, Pablo Kratter, Kaitlin M. |
| contents | 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 (IMEX) 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 multi-fluid 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_04435 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Fast second-order solver for stiff multifluid dust and gas hydrodynamics Krapp, Leonardo Garrido-Deutelmoser, Juan Benítez-Llambay, Pablo Kratter, Kaitlin M. Computational Physics Earth and Planetary Astrophysics High Energy Astrophysical Phenomena Instrumentation and Methods for Astrophysics Solar and Stellar Astrophysics 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 (IMEX) 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 multi-fluid 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. |
| title | A Fast second-order solver for stiff multifluid dust and gas hydrodynamics |
| topic | Computational Physics Earth and Planetary Astrophysics High Energy Astrophysical Phenomena Instrumentation and Methods for Astrophysics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2310.04435 |