We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H1 initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H1 towards a dissipative weak solution of C...

Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by varying degrees of memory and computational intensity, are evaluated in the context of finite difference methods for fluid dynamics problems. It is shown that, ...

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H towards a dissipative weak solution of Cam...

[1] In drainage basin evolution models the implementation of sediment transport and sediment balance is constrained by numerical instabilities. In order to overcome these difficulties an implicit finite difference method is proposed. The method simultaneously adjusts the elevation at each node of the numerical grid, is unconditionally stable, and significantly reduces the computational time. Th...

NASA/TM—2013-217850 1 ∆t∗ nondimensional time step, ∆t/(L/V0) kinetic energy dissipation rate 1 kinetic energy dissipation rate computed from deviatoric strain rate 3 kinetic energy dissipation rate computed from pressure dilatation κ angular wave number μ kinematic viscosity ν spectroscopic wave number ωi vorticity vector Ω volume ρ density σ filter damping coefficient τij stress tensor ζ enst...

Balanced restoration consists in removing the effects of tectonic deformation in order to recover the depositional state of sedimentary layers. Restoration thus helps in the understanding of a geodynamic scenario, reduces structural uncertainties by testing the consistency of the structural model, and, under mechanical behavior assumptions, evaluates retro-deformation. We show how an elastic fi...