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In physically inviscid fluid dynamics, ‘shock‐capturing’ methods adopt either an artificial viscosity contribution or an appropriate Riemann‐solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations if flow discontinuities (the Riemann problem) are to be solved. A necessary dissipation is normally used in such cases. An explicit artificial viscosity contribution is normally adopted to smooth out spurious heating and to treat transport phenomena. Such a treatment of inviscid flows is also widely adopted in the smooth particle hydrodynamics (SPH) finite‐volume free Lagrangian scheme. In other cases, the intrinsic dissipation of Godunov‐type methods is implicitly useful. Instead, ‘shock‐tracking’ methods normally use the Rankine–Hugoniot jump conditions to solve such problems. A simple, effective solution of the Riemann problem in inviscid ideal gases is proposed here, based on a reformulation of the equation of state (EoS) in the Euler equations in fluid dynamics, the limit of which for a motionless gas coincides with the classical EoS of ideal gases. The application of such an effective solution to the Riemann problem excludes any dependence, in the transport phenomena, on particle‐smoothing resolution length  h  in non‐viscous SPH flows. Results for one‐dimensional shock‐tube tests, as well as examples of application for two‐dimensional shear flows, are shown here. As an astrophysical application, a much better identification of spiral structures in accretion discs in a close binary (CB) as a result of this reformulation is also shown here.

monthly notices of the royal astronomical society

An approach to the Riemann problem in the light of a reformulation of the state equation for SPH inviscid ideal flows: a highlight on spiral hydrodynamics in accretion discs