Numerical methods for solving the Navier-Stokes equation

Navier-Stokesova jednadžba opisuje gibanje viskoznih fluida. Korisna je pri opisu fizikalnih procesa u problemima koji su zanimljivi u znanosti i inženjerstvu. Dinamika fluida je grana fizike koja je, uz zakone termodinamike, opisana Navier-Stokesovom jednadžbom i jednadžbom kontinuiteta. Analitičko rješenje spometnutih jednadžbi je poznato samo za jednostavne slučajeve. Stoga, u rješavanju Navier-Stokesove jednadžbe veliku ulogu imaju numeričke metode. U ovom radu se bavimo podgranom dinamike fluida koja se zove računalna dinamika fluida. Računalna dinamika fluida podrazumijeva korištenje numeričkih metoda za rješavanje problema toka fluida te se često primjenjuje kao alat za validaciju jednostavnijih modela. U ovom radu koristit ćemo računalnu dinamiku fluida u svrhu validacije modela rashladnog sustava električnog vozila. Rashladni sustav električnog vozila modeliramo na osnovi fizikalnih jednadžbi uzimajući u obzir najrelevantnije geometrijske veličine. Model, koji će biti pisan u C++ programskom jeziku, treba biti jednostavan i imati kratko vrijeme izvođenja. Zasebno modelirane komponente ćemo spojiti u rashladni sustav. Tada, cijeli rashladni sustav kao zasebnu jedinicu spajamo sa softverom AVL VSM koji služi za simulacije dinamike vozila. Pokretanjem simulacija vožnje određene putanje, promatrat ćemo utjecaj rashladnog sustava na temperaturu ćelije i posljedično performanse vozila. Rezultate za pojedinu komponentu modeliranog rashladnog sustava ćemo usporediti sa rezultatima koji se dobiju koristeći računalnu dinamiku fluida.Navier-Stokes equation describes the motion of viscous fluids. It is useful in describing physical processes in problems of interest in science and engineering. Fluid dynamics is a branch of physics which, along with the laws of thermodynamics, is described by the Navier-Stokes equation and the continuity equation. The analytical solution of the mentioned equations is known only in simple cases. Therefore, numerical methods play a major role in solving the Navier-Stokes equation. In this thesis, we deal with a sub-branch of fluid dynamics called computational fluid dynamics. Computational fluid dynamics involves the use of numerical methods to solve fluid flow problems and is often used as a tool in validating simpler models. In this thesis, we will use computational fluid dynamics for the purpose of validating a cooling system model of an electric vehicles. The cooling system of an electric vehicle is modeled on the basis of physical equations taking into account the most relevant geometric quantities. The model, which will be written in the C ++ programming language, should be simple and have a short execution time. Separately modelled components will be connected to the cooling system. Then, the entire cooling system as a separate unit is connected to the AVL VSM software, which is used to simulate vehicle dynamics. By running driving simulations of a certain maneuver, we will observe the influence of the cooling system on the cell temperature and consequently the vehicle performance. The results for each component of the modeled cooling system will be compared with the results obtained using computational fluid dynamics