SENR/NRPy+ : Numerical relativity in singular curvilinear coordinate systems

1 8 Ja n 20 06 Orthogonal curvilinear coordinate systems corresponding to singular spectral curves ∗

an 2 00 6 Orthogonal curvilinear coordinate systems corresponding to singular spectral curves ∗

Coordinate Conditions and Their Implementation in 3D Numerical Relativity

We put forth a few ideas on coordinate conditions and their implementation in numerical relativity. Coordinate conditions are important for the long time scale simulations of relativistic systems, e.g., for the determination of gravitational waveforms from astrophysical events to be measured by LIGO/VIRGO. We demonstrate the importance of, and propose methods for, the active enforcement of coor...

Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems

In this article, we present efficient and stable numerical schemes to simulate threedimensional quantum dot with irregular shape, so that we can compute all the bound state energies and associated wave functions. A curvilinear coordinate system that fits the target quantum dot shape is first determined. Three finite difference discretizations of the Schrödinger equation are then developed on th...

Performance of WENO Scheme in Generalized Curvilinear Coordinate Systems

The weighted-essentially non-oscillatory (WENO) schemes have been used to calculate the shock-embedded compressible fluid flow ([9]). The potential high-fidelity qualities of this approach make it attractive for jet noise simulation. However, in its present form, the WENO procedure has many drawbacks that prevent direct applications to jet noise simulations. In this paper, various WENO procedur...