Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Investigation of Numerical Diffusion in Aerodynamic Flow Simulations
  with Physics Informed Neural Networks   Computational Fluid Dynamics (CFD) simulations are used for many air flow
simulations including road vehicle aerodynamics. Numerical diffusion occurs
when local flow direction is not aligned with the mesh lines and when there is
a non-zero gradient of the dependent variable in the direction normal to the
streamline direction. It has been observed that typical numerical
discretization schemes for the Navier-Stokes equations such as first order
upwinding produce very accurate solutions without numerical diffusion when the
mesh is aligned with the streamline directions. On the other hand, numerical
diffusion is maximized when the streamline direction is at an angle of 45{\deg}
relative to the mesh line. The amount of numerical diffusion can be reduced by
mesh refinements such as aligning mesh lines along the local flow direction or
by introducing higher order numerical schemes which may introduce potential
numerical instability or additional computational cost. Couple test cases of a
simple steady-state incompressible and inviscid air flow convection problem
were used to investigate whether numerical diffusion occurs when using Physics
Informed Neural Networks (PINNs) that rely on automatic differentiation as
opposed to numerical techniques used in traditional Computational Fluid
Dynamics (CFD) solvers. Numerical diffusion was not observed when PINNs were
used to solve the Partial Differential Equation (PDE) for the simple convection
problem irrespective of flow angle. The PINN correctly simulated the streamwise
upwinding, which has great potential to improve the accuracy of Navier-Stokes
solvers.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph