A hardly known and very important result of Kreiss is proven explicitly: Outflow boundary extrapolation, which complements stable dissipative schemes for linear hyperbolic initial value problems, maintains stability. In view of this result, the Lax-Wendroff and the Gottlieb-Turkel schemes are applied to a test problem. As expected from the rate-of-convergence theory by Gustafsson, global order ...

We study complex-valued symmetric matrices. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. Consequently, we provide a sharp criterion for identifying those symmetric matrices whose spectral norm does not exceed one: such strongly stable matrices are usually sought in connection with convergent difference approximations ...

We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version unstructured meshes, including uniform triangular and hexagonal meshes non-uniform polygonal The performance of the is ...

The typical equation for bed level change in sediment transport in river, estuary and near shore systems is based on conservation of sediment mass. It is generally a nonlinear conservation equation for bed level. The physics here are similar to shallow water wave equations and gas dynamics equation which will develop shock waves in many circumstances. Many state-of-art morphological models use ...

Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain "tension" parameters associated with the exponential spline allows the sharp resolution of shocks and the suppression of any attendant oscil...

In this paper, the Lax-Wendroff difference scheme has been presented for solving one-dimensional wave equation with integral boundary conditions. First, given solution domain is discretized and derivative involving spatial variable replaced by central finite approximation of functional values at each grid point using Taylor series expansion. Then, resulting second-order linear ordinary differen...

In [18], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws on a Cartesian mesh, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax-W...

We develop an alternative formulation of conservative finite difference weighted essentially non-oscillatory (WENO) schemes to solve conservation laws. In this formulation, the WENO interpolation of the solution and its derivatives are used to directly construct the numerical flux, instead of the usual practice of reconstructing the flux functions. Even though this formulation is more expensive...