Numerical methods:

Interface tracking methods (Level Set); Structured Adaptive Mesh Refinement (SAMR); high-order-accurate shock-capturing (Finite-Volume, Discontinuous Galerkin) schemes (hyperbolic conservation laws), projection methods, lattice-Boltzmann methods (incompressible flows), spectral methods (linear stability theory), Jacobian-Free Newton-Krylov methods, Physics-Based Preconditioning (PBP).

Modeling of turbulent and multiphase flows:

Direct Numerical Simulation (DNS) of incompressible and compressible multifluid flows; Sharp-Interface Methods (SIM); effective field; hyperbolicity/ill-posedness of time-, space- and ensemble-averaged equations; DNS, LES and RANS modeling of turbulent natural convection flows.

Physics of complex high-speed and multiphase flows:

Shock wave refraction and pattern formation at fluid-fluid and fluid-solid interfaces; linear theory for interfacial instabilities (Rayleigh-Taylor and Kelvin-Helmholtz); shock-wave-induced shattering of gas-liquid and gas-solid interfaces; high-speed/explosion-induced dispersion of liquid and solid material.

Application of CFD to design and safety of engineering systems:

Simulation and prediction of accident-related phenomena in nuclear and chemical reactors; design and analysis of safety measures preventing/ mitigating or terminating accident sequences; design and optimization of advanced high-energy devices and systems.