Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shock capturing by anisotropic diffusion oscillation reduction   This paper introduces the method of anisotropic diffusion oscillation
reduction (ADOR) for shock wave computations. The connection is made between
digital image processing,in particular, image edge detection, and numerical
shock capturing. Indeed, numerical shock capturing can be formulated on the
lines of iterative digital edge detection. Various anisotropic diffusion and
super diffusion operators originated from image edge detection are proposed for
the treatment of hyperbolic conservation laws and near-hyperbolic hydrodynamic
equations of change. The similarity between anisotropic diffusion and
artificial viscosity is discussed. Physical origins and mathematical properties
of the artificial viscosity is analyzed from the kinetic theory point of view.
A form of pressure tensor is derived from the first principles of the quantum
mechanics. Quantum kinetic theory is utilized to arrive at macroscopic
transport equations from the microscopic theory. Macroscopic symmetry is used
to simplify pressure tensor expressions. The latter provides a basis for the
design of artificial viscosity. The ADOR approach is validated by using
(inviscid) Burgers' equation in one and two spatial dimensions, the
incompressible Navier-Stokes equation and the Euler equation. A discrete
singular convolution (DSC) algorithm is utilized for the spatial
discretization.

3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg