This paper proposes a novel locally adaptive pseudo-time stepping convergence acceleration technique for dual time stepping which is a common integration method for solving unsteady low-Mach preconditioned/incompressible
Navier-Stokes formulations. In contrast to standard local pseudo-time stepping techniques that are based on computing the local pseudo-time steps
directly from estimates of the local Courant-Friedrichs-Lewy limit, the proposed technique controls the local pseudo-time steps using local truncation
errors which are computed with embedded pair RK schemes. The approach
has three advantages. First, it does not require an expression for the characteristic element size, which are difficult to obtain reliably for curved mixedelement meshes. Second, it allows a finer level of locality for high-order
nodal discretisations, such as FR, since the local time-steps can vary between solution points and field variables. Third, it is well-suited to being
combined with P-multigrid convergence acceleration. Results are presented
for a laminar 2D cylinder test case at Re = 100. A speed-up factor of 4.16
is achieved compared to global pseudo-time stepping with an RK4 scheme,
while maintaining accuracy. When combined with P-multigrid convergence
acceleration a speed-up factor of over 15 is achieved. Detailed analysis of
the results reveals that pseudo-time steps adapt to element size/shape, solution state, and solution point location within each element. Finally, results
are presented for a turbulent 3D SD7003 airfoil test case at Re = 60, 000.
Speed-ups of similar magnitude are observed, and the flow physics is found
to be in good agreement with previous studies.