Curvilinear Coordinate
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Related Articles from SNS
High-Order Summation-By-Parts Schemes for First-Order Hyperbolic Systems in Curvilinear Coordinates with Singularities
Announce Type: cross Abstract: Formulating stable numerical methods for hyperbolic systems in curvilinear coordinate with singularities, e.g. spherical coordinates, is complicated by the presence of these singularities. We present a method for constructing high-order accurate, energy-stable finite difference operators satisfying the Summation-by-Parts (SBP) property on spherical domains, extending ideas presented by [C. Gundlach, J. M. Mart\'in-Garc\'ia, and D. Garfinkle, CQG 30, 145003 (2013)].
A Generalised Curvilinear Coordinate system-based Patch Dynamics Scheme in Equation-free Multiscale Modelling
arXiv:2405.08764v2 Announce Type: replace Abstract: The patch dynamics scheme in equation-free multiscale modelling has the potential to efficiently predict the macroscopic behaviours by simulating the microscale problem in a fraction of the space-time domain. The patch dynamics schemes developed so far are mainly on rectangular domains with uniform grids and uniform rectangular patches. In real-life problems, the geometry of the domain is not regular or simple, where rectangular and uniform...
3d Summation-by-Parts scheme for Linear Wave Equations on Hyperboloidal Slices
arXiv:2606.02051v1 Announce Type: cross Abstract: We derive a fully 3-dimensional Summation-By-Parts scheme for a class of linear wave equations on hyperboloidal slices that meet future null infinity on a Minkowski background. The scheme is derived in spherical polar coordinates, with a major strength being that it is provably stable and allows having grid points at the origin and on the $z$-axis, despite coordinate singularities, and at infinity, by introducing compactification followed by...