A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh

Abstract

We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable axisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios, and quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima (1986) and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. (1994). When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows, such as accretion disks and mass-transferring binary systems.

A new class of accurate, mesh-free hydrodynamic simulation methods

“…Davis 1984). For example, (Hahn et al 2010) study cosmological simulations of galaxies in AMR and find that the galaxy spin axes are strongly aligned with the grid axes by low redshift, even at "effective" resolutions of ∼ 128 2 − 512 2 in the disk plane (particle numbers in the disk up to 5 × 10 5 ); Byerly et al (2014) demonstrate similar grid alignment and disk destruction effects in AMR simulations of stellar evolution and binary orbits up to AMR resolutions of ∼ 1024 3 . A variety of coordinate "patch" schemes or hybrid advection schemes have been designed to reduce these errors, but these all rely on some prior knowledge of the computational geometry.…”

White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification

“…We wish to emphasize that although it is commonly stated in the literature that fixed-mesh codes poorly conserve angular momentum, it is only generally true that mesh-based codes do not exactly conserve angular momentum when the equations are written in conservative form for linear momentum. Indeed, Motl et al (2002) and Byerly et al (2014) have evolved binary systems using the hydrodynamics equations written in a form that explicitly conserves angular momentum, and it is straightforward to convert an existing grid-based code to solve the system of equations that Byerly et al (2014) present. Additionally, the extent to which angular momentum conservation is violated in our code is a function of the resolution.…”

Harnessing billions of tasks for a scalable portable hydrodynamic simulation of the merger of two stars

“…In this article, we detail programming model updates to create OctoTiger, a three-dimensional (3-D) finitevolume octree AMR hydrodynamics code with Newtonian gravity (Marcello et al, 2016;STE||AR Group, 2017d). It is a successor to previous codes described by Byerly et al (2014), D'Souza et al (2006, Kadam et al (2016), Lelbach et al (2013), Lindblom et al (2001), Motl et al (2007Motl et al ( , 2017, Ott et al (2005), and STE||AR Group (2017c). In OctoTiger, the astrophysical fluid is modeled using the inviscid Euler equations.…”