  In dwarf nov{\ae} and low-mass X-ray binaries, the tidal potential excites
spiral waves in the accretion disc. Spiral wave driven accretion may be
important in quiescent discs, where the angular momentum transport mechanism
has yet to be identified. Previous studies were limited to unrealistically high
temperatures for numerical studies or to specific regimes for analytical
studies. We perform the first numerical simulation of spiral wave driven
accretion in the cold temperature regime appropriate to quiescent discs, which
have Mach numbers > 100. We use the new GPU-accelerated finite volume code
Idefix to produce global hydrodynamics 2D simulations of the accretion discs of
dwarf nov{\ae} systems with a fine-enough spatial resolution to capture the
short scale-height of cold, quiescent discs with Mach numbers ranging from 80
to 370. Running the simulations on timescales of tens of binary orbits shows
transient angular momentum transport that decays as the disc relaxes from its
initial conditions. We find the angular momentum parameter {\alpha} drops to
values << 0.01 , too weak to drive accretion in quiescence.
