Ivan Christov

a) Complex and Nonlinear Systems: the study of the mechanics of natural phenomena using advanced mathematical techniques and state-of-the-art computational simulations; in particular: diffusion, mixing and self-organization of granular matter, flow in heterogeneous porous media, multiphase interfacial instabilities, fluid–structure interactions, shock-formation in compressible flows, viscoelastic flows and non-Newtonian rheology, dynamics of coherent structures in nonlinear wave equations, nonlinear Fourier analysis of physical data.

b) Numerical Methods/Analysis: the development of high-performance reliable simulation techniques for real-world applications; in particular: Godunov-type schemes for conservation laws and Hamilton–Jacobi equations, segregated two-way-coupled finite-volume approaches to viscous fluid‐structure interactions, finite-volume methods for reservoir simulation, implicit conservative finite-difference and finite element methods for nonlinear diffusion and nonlinear wave equations.