#### Fundamental studies

**Hydrodynamic instabilities and the transition to turbulence:** onset of 3D in fluid flows which allow for 2D solutions.

Physical mechanisms for the onset of 3D vortex structures in the wake (mode A instability) [in preparation].
The action of basic physical mechanisms causing the growth/decay of 3D vortex structures [Aleksyuk, Shkadov, EJMB/F, 2018; JFS, 2019].
**Compressible flows of viscous gas:** energy separation in wakes.

The mechanism responsible for the Eckert-Weise effect [Aleksyuk, JFM, 2021].
Intensification of the energy separation in the wakes [Aleksyuk, Osiptsov, IJHMT, 2018; Aleksyuk, IJHMT, 2019].
**Shallow water flows:** Riemann problem with a discontinuous bottom.
Exact solver for the Riemann problem [Aleksyuk, Malakhov, Belikov, JCP, 2022].
The uniqueness of the Riemann problem [Aleksyuk, Belikov, JCP, 2019].
#### Applied studies

I develop mathematical models and numerical methods for applied water problems, such as modelling river flows with non-uniform sediment transport. The results of this research are implemented in the software STREAM 2D (Aleksyuk, Belikov) and used by various groups to solve environmental problems, as well as in education.

#### CFD software

I use self-developed (C++, MPI, OpenMP, CUDA) software to simulate compressible/incompressible viscous fluid flows, two-phase immiscible flows, flows in shallow water approximation, and analyse the results applying the methods of the theory of hydrodynamic stability. Algorithms are based on the finite element and finite volume methods. Calculations are carried out using supercomputers and/or graphics processing units.

#### Fundings

In the last 5 years, the work has been supported by 10 scientific grants and 6 contracts (connected to applied river flow simulations).