Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cell Size Effect on Computational Fluid Dynamics: The Limitation
  Principle for Flow Simulation   For theoretical gas dynamics, the flow regimes are classified according to
the Knudsen number. For computational fluid dynamics (CFD), the numerical flow
field is the projection of the physical flow field onto the discrete space and
time, which is related to the cell Knudsen number. The real representable flow
regimes are controlled by these two parameters. According to the values of
Knudsen number and cell Knudsen number, we study the classification of the
numerical flow regimes. In the process of mesh refinement, the numerical
experiments show the change of numerical flow regime from continuum, to
near-continuum, and to non-equilibrium one. The change of flow regime with
different cell resolution is the limitation principle for the numerical
simulation, which is the best a multiscale method can do. In other words, we
should have changeable numerical governing equations in different mesh size
scale, and they are coupled with the traditional physical equations in
different scales, such as the Navier-Stokes and Boltzmann. Under the multiscale
modeling, a mesh refinement is a process in resolving the flow physics in
different scale. The verification and validation (V$\&$V) need include the
physical modeling mechanism in the mesh refinement process. The traditional
idea of mesh refinement for targeting a fixed partial differential equation
cannot achieve the final goal of computation, which is to recover the flow
physics as truthfully as possible under the limitation of the cell resolution.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex