Boundary conditions and applications of WENO finite difference schemes for hyperbolic problems TAN, SIRUI creator 2012 xvii, 125 p. born digital Thesis (Ph.D. -- Brown University (2012) Shu, Chi-Wang Director Guzman, Johnny Reader Hesthaven, Jan Reader Brown University. Applied Mathematics sponsor theses This dissertation presents two topics concerning weighted essentially non-oscillatory (WENO) finite difference schemes for solving hyperbolic problems. In the first part, we develop a high order accurate numerical boundary condition for solving hyperbolic problems on fixed Cartesian grids, while the physical domain can be arbitrarily shaped and moving. Compared with body-fitted meshes, the biggest advantage of Cartesian grids is that the grid generation is trivial. The challenge is however that the physical boundary does not usually coincide with grid lines. The wide stencil of WENO schemes makes a stable boundary treatment even harder to realize. There are two main ingredients of our method. The first one is an inverse Lax-Wendroff procedure for inflow boundary conditions and the other one is a robust and high order accurate extrapolation for outflow boundary conditions. Our method is high order accurate, stable under standard CFL conditions determined by the interior WENO schemes, and easy to implement. It has been successfully applied to simulate interactions between compressible inviscid flows and rigid (static or moving) bodies with complex geometries. In the second part, we apply WENO finite difference schemes to solve the updated Buxton-Clarke model for organic photovoltaic cells. The model is represented by a system of convection-diffusion-reaction equations coupled to a Poisson's equation. The solution usually contains sharp gradients. WENO schemes successfully resolve the physical quantities on a relatively coarse mesh. The numerical simulations quantify the effect of material properties on device performance. WENO schemes finite difference method hyperbolic problems numerical boundary conditions boundary treatment Cartesian grid compressible flows organic photovoltaic cells Finite differences RPB 20121023 engEnglish10.7301/Z07942Z7In CopyrightCollection is open for research.dissertations