An unconditionally stable implicit method for hyperbolic conservation laws

Abstract

We construct a space-centered self-adjusting hybrid difference method for one-dimensional hyperbolic conservation laws. The method is linearly implicit and combines a newly developed minimum dispersion scheme of the first order with the recently developed second-order scheme of Lerat. The resulting method is unconditionally stable and unconditionally diagonally dominant in the linearized sense. The method has been developed for quasi-stationary problems, in which shocks play a dominant role. Numerical results for the unsteady Euler equations are presented. It is shown that the method is non-oscillatory, robust and accurate in several cases.

Transient behavior of pulsed particulate fluidized beds

“…Both models consist of single or multiple nonlinear, coupled hyperbolic partial differential equations that have to be solved numerically. An implicit finite difference method for hyperbolic conservative-law equations as derived by Wilders (1985) is adopted for this purpose. The computational results of both models are compared to experimental data obtained in a laboratory-scale multistage fluidized bed.…”

“…The numerical solution by the finite difference technique of Wilders (1985) requires that the set of Eqs. 1-4 is rewritten as a set of general conservation-law equations:…”

“…Both models were solved numerically by the method described by Wilders (1985). The position of the bed end varies with time and cannot coincide with the end of a spatially fixed computational domain.…”