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

Understand

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.