Numerical modelling of unsteady high-speed compressible flows

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The research program is concerned with essentially unsteady high-speed multi-dimensional compressible flows, which are much less explored in compressible fluid dynamics than steady phenomena and, likewise, accurate and efficient numerical methods and codes for them are few in number. New numerical methods and computer codes specifically tailored for unsteady, multi-scale, multi-fluid flows with spatially-localized features (shock waves, contact surfaces, boundary layers, vortices etc.) will be developed on the basis of the previous work by the principal investigator on locally adaptive unstructured finite-volume Euler (inviscid) solvers for non-reacting gas mixtures. Three major generalizations are to be undertaken: (1) For unsteady viscous flows at high Reynolds numbers in which viscosity effects are confined to shock fronts, boundary layers and separation zones, contact surfaces; (2) For mixtures of fluids with various equations of state (Tait, JWL etc.) (3) For nonlinear acoustics problems in heterogenous media. The research program will encompass the following application areas: (I) Basic studies of shock wave reflections, in particular on the influence of viscosity and heat conductivity on shock wave reflections; (II) Starting of air inlets of hypersonic air-breathing engines (scramjets), including recenlty proposed innovative techniques (diapgragm rupture, accelerative starting); (III) Flow dynamics in gas/explosive systems. (a) Channel effect problem (when an explosive layer is detonated inside a planar or axisymmetrical channel) which has many applications in mining, aerospace, high-pressure physics and other fields; (b) Different concepts of hypervelocity launchers in which the enormous energy densities of high explosives is used to accelerate projectiles to hypervelocities, which can be applied to high-speed impact tests (e.g. when testing satellite bumper shields); (IV) Non-linear waves in heterogenous media. In this area the developed computational method will be used for simulations of wave phase conjugation in acoustics with practical applications in echography of biological tissues, non-destructive testing, magneto-acoustics etc.