  We conduct three-dimensional hydrodynamical simulations of common envelope
jets supernova (CEJSN) events where we assume that a neutron star (NS) launches
jets as it orbits inside the outer zones of a red supergiant (RSG) envelope,
and find the negative jet feedback coefficient to be ~0.1-0.2. This coefficient
is the factor by which the jets reduce the mass accretion rate onto the NS as
they remove mass from the envelope and inflate bubbles (cocoons). Our results
suggest that in most CEJSN events the NS-RSG binary system experiences the
grazing envelope evolution (GEE) before it enters a full common envelope
evolution (CEE). We also find that the jets induce upward and downward flows in
the RSG envelope. These flows together with the strong convection of RSG stars
might imply that energy transport by convection in CEJSNe is very important.
Because of limited numerical resources we do not include in the simulations the
gravity of the NS, nor the accretion process, nor the jets launching process,
and nor the gravity of the deformed envelope. Future numerical simulations of
CEE with a NS/BH companion should include the accretion process onto the NS
(and vary the jets' power accordingly), the full gravitational interaction of
the NS with the RSG, and energy transport by the strong convection.
