Applications of theoretical physics: Matter at high pressures and transonic aerodynamics

Intense activities have been executed at the Institute of Physics in the eighties of the past century on two applied physics projects: "Matter under high pressure" and "Transonic aerodynamics". In the first project the methods of the empirical and ab-initio pseudopotentials, as well as the localized muffin-tin orbitals (LMTO), were used for the calculation of the band structure of different metals under high pressure. The results were used to write the equations of state for these materials, and to compare them with the statistical equations of state at high pressures, based on the Thoinas-Fermi-Dirac model with corrections, and with the experimental results. In the second project a numerical method was implemented for analyzing the transonic potential flow past a lifting, swept wing based oil the finite-difference solutions of the full potential, and also Euler equations. In the case of the full potential equation, the method was based on the FLO algorithm, developed at the Princeton University. The metod uses a finite-difference approximation of the corresponding equations, and a coordinate system that is nearly conformally mapped from the physical space in planes parallel to the symmetry plane, and reduces the wing surface to a portion of one boundary of the computational grid. A rotated coordinate invariant difference scheme is used, and the difference equations are solved by relaxation. The method is capable of treating wings of arbitrary planform and dihedral. Approximate treatment of tip effect and vortex sheet is also included.