Forces on Bins - The Effect of Random Friction

In this note we re-examine the classic Janssen theory for stresses in bins, including a randomness in the friction coefficient. The Janssen analysis relies on assumptions not met in practice; for this reason, we numerically solve the PDEs expressing balance of momentum in a bin, again including randomness in friction.Comment: 11 pages, LaTeX, with 9 figures encoded, gzippe

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

Adaptive Sparse Grids for Hyperbolic Conservation Laws

. We report on numerical experiments using adaptive sparse grid discretization techniques for the numerical solution of scalar hyperbolic conservation laws. Sparse grids are an efficient approximation method for functions. Compared to regular, uniform grids of a mesh parameter h contain h \Gammad points in d dimensions, sparse grids require only h \Gamma1 jloghj d\Gamma1 points due to a truncated, tensor-product multi-scale basis representation. For the treatment of conservation laws two different approaches are taken: First an explicit time-stepping scheme based on central differences is introduced. Sparse grids provide the representation of the solution at each time step and reduce the number of unknowns. Further reductions can be achieved with adaptive grid refinement and coarsening in space. Second, an upwind type sparse grid discretization in d + 1 dimensional space-time is constructed. The problem is discretized both in space and in time, storing the solution at all time st..

Comparison of two conservative schemes for hyperbolic interface problems

Abstract. We recall two conservative schemes recently proposed for the numerical solution of hyperbolic interface problems. Then, we compare the two schemes on a piston problem and a shock tube problem.

A Lagrangian central scheme for multi-fluid flows

We develop a central scheme for multi-fluid flows in Lagrangian coordinates. The main contribution is the derivation of a special equation of state to be imposed at the interface in order to avoid non-physical oscillations. The proposed scheme is validated by solving several tests concerning one-dimensional hyperbolic interface problems

High-Order Central Schemes For Hyperbolic Systems Of Conservation Laws

. A family of shock capturing schemes for the approximate solution of hyperbolic systems of conservation laws is presented. The schemes are based on a modified ENO reconstruction of pointwise values from cell averages and on approximate computation of the flux on cell boundaries. The use of a staggered grid avoids the need of a Riemann solver. The integral of the fluxes is computed by Simpson's rule. The approximation of the flux on the quadrature nodes is obtained by Runge-- Kutta schemes with the aid of natural continuous extension (NCE). This choice gives great flexibility at low computational cost. Several tests are performed on the scalar equation and on systems. The numerical results confirm the expected accuracy and the high resolution properties of the schemes. Key words. conservation laws, central schemes, high order, Runge--Kutta AMS subject classifications. 65M10, 65M05 PII. S1064827597324998 1. Introduction. In this paper we present third- and fourth-order central schemes f..