• Corpus ID: 246210345

Approximating moving point sources in hyperbolic partial differential equations

@article{Rydin2022ApproximatingMP,
  title={Approximating moving point sources in hyperbolic partial differential equations},
  author={Ylva Rydin and Martin Almquist},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.08658}
}
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point sources, however, pose two challenges that do not appear in the stationary case. First, the discrete source must not excite modes that propagate with the source velocity. Second, the discrete source spectrum amplitude must be independent of the source position. We… 

References

SHOWING 1-10 OF 17 REFERENCES
Discretizing singular point sources in hyperbolic wave propagation problems
Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations
An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid, consisting of a set of structured rectangular component grids with
High-fidelity Sound Propagation in a Varying 3D Atmosphere
TLDR
A stable and high-order accurate upwind finite difference discretization of the 3D linearized Euler equations is presented, which leads to robust and accurate numerical approxims in the presence of point sources and naturally avoids the onset of spurious oscillations.
On the approximation of singular source terms in differential equations
We study differential equations with singular source terms. For such equations classical convergence results do not apply, as these rely on the regularity of the solution and the source terms. We
The immersed boundary method
This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes
Abstract We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for
Time-Dependent Problems and Difference Methods
...
...