  Motivated by the work on stagnation-point type exact solutions (with infinite
energy) of 3D Euler fluid equations by Gibbon et al. (1999) and the subsequent
demonstration of finite-time blowup by Constantin (2006) we introduce a
one-parameter family of models of the 3D Euler fluid equations on a 2D symmetry
plane. Our models are seen as a deformation of the 3D Euler equations which
respects the variational structure of the original equations so that explicit
solutions can be found for the supremum norms of the basic fields. The value of
the model's parameter determines if there is finite-time blowup, and the
singularity time can be computed explicitly in terms of the initial conditions
and the model's parameter. We use a representative parameter value, for which
the solution blows up in finite-time, as a benchmark for the systematic study
of errors in numerical solutions. We compare numerical integrations of our
"original" model with a "mapped" version of these equations. The mapped version
is a globally regular (in time) system of equations, obtained via a bijective
nonlinear mapping of time and fields from the original model equations
(Bustamante 2011). We show that the mapped system's numerical solution
increases accuracy in estimates of supremum norms and singularity time while
entailing only a small additional computational cost. We study the Fourier
spectrum of the model's numerical solution and find that the analyticity-strip
width (a measure of the solution's analyticity) tends to zero as a power law in
a finite time. This is in agreement with the finite-time blowup of the supremum
norms, in the light of rigorous bounds stemming from the bridge (Bustamante &
Brachet 2012) between the analyticity-strip method and the Beale-Kato-Majda
type of theorems. We conclude by discussing the implications of this research
on the analysis of numerical solutions of the 3D Euler fluid equations.

Fluid Dynamics