The highly involved macroscopic low-frequency dynamics of partially io
nized dusty plasmas can be studied by means of computational fluid sim
ulations. We derived a general set of numerically tractable balance eq
uations taking into account mass, momentum and energy conservation. On
the grounds of these equations we developed a quasi-neutral compressi
ble three-dimensional multi-fluid code that integrates the closed set
of equations for the electron, ion, dust and neutral components. The i
ntegration scheme of this explicit code (DENISIS = Dust Electron Neutr
al Ion Self-consistent Integration Scheme) is based on the Leapfrog an
d Dufort-Frankel method modified by a numerically damped treatment of
the nonconservative terms in the balance equations. The applicability
of the code is illustrated by modelling characteristic plasma phenomen
a as wave and instability processes. (C) 1998 Elsevier Science B.V.