Izvleček
Zaradi hitrih osebnih računalnikov so postale Monte Carlo simulacije v teoretični znanosti in tudi v praksi zelo popularne. Z njimi raziskujemo naključne pojave v naravi in družbi, ki so za izključno analitično obravnavo prezapleteni. Med zelo zahtevne fizikalne probleme spadajo tudi naloge s področja aerodinamike in hidrodinamike. Zato jih navadno rešujejo s kombiniranjem numeričnih simulacij in eksperimentov, na primer z uporabo vetrovnikov. Pri gibanju telesa skozi kapljevino ali plin se pojavi upor sredstva, za katerega pri dovolj majhnih hitrostih dobro velja linearni zakon upora (sorazmernost sile s hitrostjo telesa), pri velikih hitrostih pa kvadratni zakon (sorazmernost sile s kvadratom hitrosti telesa). Oba zakona dosledno izpeljemo iz Navier-Stokesove nelinearne parcialne diferencialne enačbe oziroma iz njenih približkov. Pri gibanju telesa skozi idealni plin pa lahko silo upora ocenimo tudi iz mikroskopske slike. Tako smo naredili v naši Monte Carlo simulaciji in pri tem med seboj povezali različne vede: statistično termodinamiko, mehaniko in numerične metode.
Abstract
Monte Carlo Simulation of Drag
Powerful personal computers made Monte Carlo simulations very popular in theoretical science and in practice. They are used to investigate probabilistic phenomena in nature and society which are too complex to be solved using a purely analytical approach. Tasks from the field of aerodynamics and hydrodynamics also belong to the class of very demanding physical problems. Therefore, they are usually solved with a combination of numerical simulations and experiments, e.g. using wind tunnels. When an object moves through liquid or gas it experiences drag, to which the linear law (force is proportional to the velocity of the object) applies for low enough velocities, while for high velocities the quadratic law applies (force is proportional to the square of the velocity of the object). Both laws can be logically derived from the Navier–Stokes nonlinear partial differential equation, i.e. from its approximations. However, when the object moves through an ideal gas, the drag force can also be estimated from the microscopic picture. This has been done in the present Monte Carlo simulation, in the process integrating different sciences: statistical thermodynamics, mechanics and numerical methods.