Some of the numerical solutions of one-dimensional Burgers' equation
| Autor: | Pavičić Donkić, Mihaela |
|---|---|
| Přispěvatelé: | Zoranić, Larisa, Stipanović, Petar, Weber, Ivana |
| Jazyk: | chorvatština |
| Rok vydání: | 2019 |
| Předmět: | |
| Popis: | Burgersova jednadžba nerijetko se susreće u pojednostavljivanju složenih modela u fizici. Pritom opisuje idealni sustav čije je razumijevanje temeljno za kasnije razumijevanje složenijih sustava. U ovom radu je kao primjer prikazano pojednostavljenje Navier-Stokes jednadžbi. Glavni cilj rada je numeričko rješavanje Burgersove jednadžbe u programskom jeziku C. Pritom se koriste dvije metode: prva metoda je kombinacija Fourierovog razvoja u red te Hopf-Cole transformacije koja Burgersovu jednadžbu svodi na jednadžbu topline, dok se druga metoda temelji na Eulerovoj metodi prema naprijed. Rješenja dobivena prvom metodom nazivaju se točna rješenja te nam time koriste za usporedbu rješenja dobivenih Eulerovom metodom. Burgers’ equation is often encountered in simplifying complex cases in physics. In doing so, it is describing an ideal system whose understanding is fundamental to later understanding of more complex systems. In this paper is presented, as an example, a simplification of the Navier-Stokes equations. The main objective of the paper is to numerically solve the Burgers equation in programming language C. Two methods are used: the first method is a combination of Fourier series and the Hopf-Cole transformation that reduces the Burgers equation to the heat equation, while the second method is based on the Euler forward method. The solutions obtained by the first method are called exact solutions and are thus used to compare the solutions obtained by the Euler method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|