  We present VAH, a (3+1)-dimensional simulation that evolves the
far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion
collisions with anisotropic fluid dynamics. We solve the hydrodynamic equations
on an Eulerian grid using the Kurganov-Tadmor algorithm in combination with a
new adaptive Runge-Kutta method. Our numerical scheme allows us to start the
simulation soon after the nuclear collision, largely avoiding the need to
integrate it with a separate pre-equilibrium dynamics module. We test the
code's performance by simulating on the Eulerian grid conformal and
non-conformal Bjorken flow as well as conformal Gubser flow, whose
(0+1)-dimensional solutions are precisely known. Finally, we compare
non-conformal anisotropic hydrodynamics to second-order viscous hydrodynamics
in central Pb+Pb collisions and find that the former's longitudinal flow
profile responds more consistently to the fluid's gradients along the spacetime
rapidity direction.
