  Computational Fluid Dynamics (CFD) simulation by the numerical solution of
the Navier-Stokes equations is an essential tool in a wide range of
applications from engineering design to climate modeling. However, the
computational cost and memory demand required by CFD codes may become very high
for flows of practical interest, such as in aerodynamic shape optimization.
This expense is associated with the complexity of the fluid flow governing
equations, which include non-linear partial derivative terms that are of
difficult solution, leading to long computational times and limiting the number
of hypotheses that can be tested during the process of iterative design.
Therefore, we propose DeepCFD: a convolutional neural network (CNN) based model
that efficiently approximates solutions for the problem of non-uniform steady
laminar flows. The proposed model is able to learn complete solutions of the
Navier-Stokes equations, for both velocity and pressure fields, directly from
ground-truth data generated using a state-of-the-art CFD code. Using DeepCFD,
we found a speedup of up to 3 orders of magnitude compared to the standard CFD
approach at a cost of low error rates.
