An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids

Müller, Bernhard; Chan, Conrad

doi:10.3847/1538-4357/aaf100

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…For time marching, we apply the second-order Crank–Nicolson method to the viscous term. A simplified-marker-and-cell algorithm (Amsden & Harlow 1970) satisfies the momentum equation (2.5) simultaneously with the solenoidal condition (2.4) by means of a direct solution to the pressure equation (Müller & Chan 2019).…”

Section: Numerical Simulationmentioning

confidence: 99%

Drag force on an oscillatory spherical bubble in shear‐thinning fluid

2023

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Power-law shear-thinning fluid motions induced by a translating spherical bubble with sinusoidal oscillation at a high frequency are numerically studied. We focus on reducing the time-averaged drag force $D$ on the bubble owing to the oscillation-enhanced shear-thinning effect. Under the assumption of negligible convection, the unsteady Stokes equation is directly solved in a finite-difference manner over a wide parameter space of the dimensionless oscillation amplitude $A$ (corresponding to the oscillatory-to-translational velocity ratio) and the power-law index $n$ of the viscosity. The results show that, for small amplitude ( $A\ll 1$ ), the drag reduction ratio $1-D/D_0$ (here, $D_0$ is $D$ with no oscillation) is proportional to $A^2$ . In contrast, for large amplitude ( $A \gg 1$ ), the drag ratio $D/D_0$ is proportional to $A^{n-1}$ , revealing a power-law behaviour. In the case of $A \gg 1$ for a strong shear-thinning fluid with small $n$ , the square of the vorticity over the entire domain is much smaller than that of the shear rate, and thus the bulk flow may be regarded as irrotational. To provide a fundamental perspective on the drag reduction mechanism, a theoretical model is proposed based on potential theory, and demonstrated to well capture the power-law relation between $D/D_0$ and $A$ .

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Section: Numerical Simulationmentioning

confidence: 99%

Drag force on an oscillatory spherical bubble in shear‐thinning fluid

2023

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“…Our parallel FFT utilizes a "transpose algorithm" known to be efficient when a data size for communication is larger than the critical size that depends on the latency/bandwidth of the interconnecting network device and the network topology (e.g., Foster & Worley 1997). An alternative "binary exchange algorithm" may work efficiently for a small data size (e.g., Müller & Chan 2019).…”

Section: Performance Testmentioning

confidence: 99%

A Fast Poisson Solver of Second-order Accuracy for Isolated Systems in Three-dimensional Cartesian and Cylindrical Coordinates

Moon

Kim

Ostriker

2019

ApJS

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We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the Athena++ magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

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Hydrodynamics of core-collapse supernovae and their progenitors

Müller¹

2020

Living Rev Comput Astrophys

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161

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Multi-dimensional fluid flow plays a paramount role in the explosions of massive stars as core-collapse supernovae. In recent years, three-dimensional (3D) simulations of these phenomena have matured significantly. Considerable progress has been made towards identifying the ingredients for shock revival by the neutrino-driven mechanism, and successful explosions have already been obtained in a number of selfconsistent 3D models. These advances also bring new challenges, however. Prompted by a need for increased physical realism and meaningful model validation, supernova theory is now moving towards a more integrated view that connects multi-dimensional phenomena in the late convective burning stages prior to collapse, the explosion engine, and mixing instabilities in the supernova envelope. Here we review our current understanding of multi-D fluid flow in core-collapse supernovae and their progenitors. We start by outlining specific challenges faced by hydrodynamic simulations of core-collapse supernovae and of the late convective burning stages. We then discuss recent advances and open questions in theory and simulations.

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An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids

Cited by 5 publications

References 38 publications

Drag force on an oscillatory spherical bubble in shear‐thinning fluid

Drag force on an oscillatory spherical bubble in shear‐thinning fluid

A Fast Poisson Solver of Second-order Accuracy for Isolated Systems in Three-dimensional Cartesian and Cylindrical Coordinates

Hydrodynamics of core-collapse supernovae and their progenitors

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