Solution of Hydrodynamic Problems Using a Universal Conservative Scheme for Transport of Conservative Admixtures Coupled with an Algorithm for Solving the Navier–Stokes Equations

An algorithm for computational hydromechanics is presented that combines an absolutely conservative transport scheme for momentum and admixtures with explicit finite-difference approximations. The study addresses key difficulties encountered when solving the full Navier–Stokes equations, including loss of conservation in certain schemes, the lack of a separate evolution equation for hydrodynamic pressure, and numerical instability. A cylindrical-coordinate formulation is described using the TIIAME conservative transport scheme together with a derived pressure evolution equation. Interactions between gas components accompanied by exothermic heat release are examined, including their influence on velocity, pressure, temperature, and admixture transport. A model computation demonstrates stable flow fields and compliance with conservation laws. The calculated distributions were not compared with experimental data; the conclusion about algorithm performance is based on numerical stability and physically expected field behaviour. The proposed approach is intended for a broad class of hydrodynamic problems, including implementations using accessible software tools.