# Artificial Viscosity

As usual in SPH ^{1} implementations, viscosity is rather an
inter-particles pressure than a bulk pressure. It was shown that the use of Equation 1 and Equation 2 generates a
substantial amount of entropy in regions of strong shear even if there is no
compression.

with

Where,
${X}_{i}$
(resp.
${X}_{j}$
) indicates the position of particle I (resp.
$j$
) and
${c}_{i}$
(resp
${c}_{j}$
) is the sound speed at location
$i$
(resp.
$j$
), and
${q}_{a}$
and
${q}_{b}$
are constants. This leads us to introduce Equation 3 and Equation 4. ^{2} The artificial viscosity is decreased in
regions where vorticity is high with respect to velocity divergence.

with

Default values for ${q}_{a}$ and ${q}_{b}$ are respectively set to 2 and 1.

^{1}Monaghan J.J.,

Smoothed Particle Hydrodynamics, Annu.Rev.Astron.Astro-phys; Vol. 30; pp. 543-574, 1992.

^{2}Balsara D.S.,

Von Neumann Stability Analysis of Smoothed Particle Hydrodynamics Suggestions for Optimal Algorithms, Journal of Computational Physics, Vol. 121, pp. 357-372, 1995.