  Exploring a variety of closing schemes to the infinite hierarchy of momentum
moments of the exactly solvable Boltzmann equation for systems undergoing
Gubser flow, we study the precision with which the resulting hydrodynamic
equations reproduce the exact evolution of hydrodynamic moments of the
distribution function. We find that anisotropic hydrodynamics, obtained by ex-
panding the distribution function around a dynamically evolving locally
anisotropic background whose evolution is matched to exactly reproduce the
macroscopic pressure anisotropy caused by the different longitudinal and
transverse expansion rates in Gubser flow, provides the most accurate
macroscopic description of the microscopic kinetic evolution. This confirms a
similar earlier finding for Bjorken flow [Moln\'ar, Niemi and Rischke, Phys.
Rev. D 94, 125003 (2016)]. We explain the physics behind this optimal matching
procedure and show that one can efficiently correct for a non- optimized
matching choice by adding a residual shear stress to the energy-momentum tensor
whose evolution is again determined by the Boltzmann equation. Additional
insights to guide the optimal choice of a macroscopic anisotropic hydrodynamic
framework for strongly-coupled systems that do not admit a microscopic kinetic
description are reported.
