A Fast second-order solver for stiff multifluid dust and gas hydrodynamics

Fuente: arXiv
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Autori principali: Krapp, Leonardo, Garrido-Deutelmoser, Juan, Benítez-Llambay, Pablo, Kratter, Kaitlin M.
Natura: Preprint
Pubblicazione: 2023
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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
id 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