In this paper we address the problem of producing an enlarged picture from a given digital image. We propose a zooming technique based on ENO and WENO schemes that are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. ENO and WENO schemes have been quite successful in applications, especially for problems containing b...

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization...

For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...

We show that the algorithm based on the weighted essentially nonoscillatory (WENO) scheme with anti-diffusive flux corrections can be used as a solver of the radiative transfer equations. This algorithm is highly stable and robust for solving problems with both discontinuities and smooth solution structures. We test this code with the ionized sphere around point sources. It shows that the WENO ...

We develop and demonstrate the capability of a high order accurate finite difference weighted essentially non-oscillatory (WENO) solver for the direct numerical simulation of transients for a two space dimensional Boltzmann transport equation (BTE) coupled with the Poisson equation modeling semiconductor devices such as the MESFET and MOSFET. We compare the simulation results with those obtaine...

In this paper, we propose a class of high-order schemes for solving oneand two-dimensional hyperbolic conservation laws. The methods are formulated in a central finite volume framework on staggered meshes, and they involve Hermite WENO (HWENO) reconstructions in space, and Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. Compared with central...

Most pharmaceutical manufacturing processes include a series of crystallization processes to increase purity with the last crystallization used to produce crystals of desired size, shape, and crystal form. The fact that different crystal forms (known as polymorphs) can have vastly different characteristics has motivated efforts to understand, simulate, and control polymorphic crystallization pr...