Comparison of high resolution method for burgers equation

Solving hyperbolic partial differential equations is extremely important for many engineering applications. These equations can be solved by analytical methods or numerical methods. Finding analytical solutions is difficult mostly impossible due to highly nonlinear nature of these equation types. On the other hand, solving hyperbolic equations numerically is relatively easy and therefore often prefered technique. Among the numerical techniques, high resolution finite volume methods have been effectively and robustly used for decades. Their high accuracy and stability features are most desirable. In this thesis, we provide literature review for certain type of high resolution methods and introduce head on comparison study of these high resolution methods. To compare the methods, we first solve scalar linear one-way wave equation. This gives us the opportunity to perform some theoretical analysis. Finally, we apply the methods to the Burgers equation. This equation is nonlinear and it can be mimic the nonlinear behavior s of the systems of the nonlinear hyperbolic equations. For instance, the Burgers equationcan accommodate shock compression or rarefaction-depression waves. Therefore, by solving the Burgers equation with different methods, we gain a lot of insights about the stability, accuracy and thus the suitibility of the certain high resolution methods.