Two-dimensional deep water waves and some problems in nonlinear optics can be described by various third order dispersive equations, modifying and generalizing the KdV as well as nonlinear… (More)

A direct Eulerian generalized Riemann problem (GRP) scheme is derived for compressible fluid flows. Riemann invariants are introduced as the main ingredient to resolve the generalized Riemann problem… (More)

Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a… (More)

This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to… (More)

Abstract. It is well-known that non-periodic boundary conditions reduce considerably the overall accuracy of an approximating scheme. In previous papers the present authors have studied a… (More)

We present a fast direct solver methodology for the Dirichlet biharmonic problem in a rectangle. The solver is applicable in the case of the second order Stephenson scheme [34] as well as in the case… (More)

Abstract. The Generalized Riemann Problem (GRP) for nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is formulated as follows: Given… (More)

We present a finite difference scheme, applicable to general irregular planar domains, to approximate the biharmonic equation. The irregular domain is embedded in a Cartesian grid. In order to… (More)

A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier–Stokes equations. The idea is to replace the vorticity in the… (More)