A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order centra...

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...

Nessyahu and Tadmor s central scheme [J. Comput. Phys. 87 (1990)] has the benefit of not using Riemann solvers for solving hyperbolic conservation laws. But the staggered averaging causes large dissipation when the time step size is small compared to the mesh size. The recent work of Kurganov and Tadmor [J. Comput. Phys. 160 (2000)] overcomes this problem by using a variable control volume and ...

Fluid-structure interaction (FSI) occurs when the dynamic water hammer forces; cause vibrations in the pipe wall. FSI in pipe systems due to Poisson and junction coupling has been the center of attention in recent years. It causes fluctuations in pressure heads and vibrations in the pipe wall. The governing equations of this phenomenon include a system of first order hyperbolic partial differen...

and we allow general boundary conditions. Solving PDEs of this generality is not routine and the success of our software is not assured. On the other hand, it is very easy to use and has performed well on a wide variety of problems. Explicit central finite difference methods are quite attractive for hyperbolic PDEs of this generality. We have implemented four: A two-step variant of the Lax-Frie...

3-D kinematical conservation laws (KCL) are equations of evolution of a propagating surface Ωt in three space dimensions and were first derived in 1995 by Giles, Prasad and Ravindran [15] assuming the motion of the surface to be isotropic. We start with a brief introduction to 3-D KCL and mention some properties relevant to this paper. The 3-D KCL, a system of 6 conservation laws, is an under-d...

Several models in mathematical physics are described by quasilin ear hyperbolic systems with source term which in several cases may become sti Here a suitable central numerical scheme for such problems is developed and application to shallow water equations Broadwell model and Extended Thermodynamics are mentioned The numerical methods are a generalization of the Nessyahu Tadmor scheme to the n...

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell averages; at the second corrector step, we ...

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (Van Leer 1977) followed by an upwind step (Roe 1981). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the N-T scheme (called ORD in Nessyahu-Tadmor 1990) and t...

The central scheme of Nessyahu and Tadmor [J. Comput. Phys., 87 (1990), pp. 408–463] solves hyperbolic conservation laws on a staggered mesh and avoids solving Riemann problems across cell boundaries. To overcome the difficulty of excessive numerical dissipation for small time steps, the recent work of Kurganov and Tadmor [J. Comput. Phys., 160 (2000), pp. 241–282] employs a variable control vo...