Mixing Sinc kernels to improve interpolations in smoothed particle hydrodynamics without pairing instability
arXiv:2307.10925 · doi:10.1093/mnras/stae216
Abstract
The smoothed particle hydrodynamic technique is strongly based on the proper choice of interpolation functions. This statement is particularly relevant for the study of subsonic fluxes and turbulence, where inherent small errors in the averaging procedures introduce excessive damping on the smallest scales. To mitigate these errors we can increase both the number of interpolating points and the order of the interpolating kernel function. However, this approach leads to a higher computational burden across all fluid regions. Ideally, the development of a single kernel function capable of effectively accommodating varying numbers of interpolating points in different fluid regions, providing good resolution and minimal errors would be highly desirable. In this work, we revisit and extend the main properties of a family of interpolators called and compare them with the widely used family of Wendland kernels. We show that a linear combination of low- and high-order Sinc kernels generates good-quality interpolators, which are resistant to pairing instability while maintaining good sampling properties in a wide range of neighbor interpolating points, . We show that a particular case of this linear mix of Sincs produces a well-balanced and robust kernel that improves previous results in the Gresho-Chan vortex experiment even when the number of neighbors is not large, while yielding a good convergence rate. Although such a mixing technique is ideally suited for Sinc kernels owing to their excellent flexibility, it can be easily applied to other interpolating families such as the B-splines and Wendland kernels.
arXiv comment16 pages, 16 figures, 4 tables, accepted by MNRAS. Added additional section and changes in several figures
References in corpus (18)
- Cosmological SPH simulations: The entropy equation
- Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
- Smoothed Particle Hydrodynamics and Magnetohydrodynamics
- Phantom: A smoothed particle hydrodynamics and magnetohydrodynamics code for astrophysics
- Smoothed Particle Hydrodynamics in Astrophysics
- Inviscid SPH
- Gasoline2: A Modern SPH Code
- SPHGal: Smoothed Particle Hydrodynamics with improved accuracy for Galaxy simulations
- SPHS: Smoothed Particle Hydrodynamics with a higher order dissipation switch
- Numerical Convergence in Smoothed Particle Hydrodynamics
- Boosting the accuracy of SPH techniques: Newtonian and special-relativistic tests
- A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies
- Improving smoothed particle hydrodynamics with an integral approach to calculating gradients
- SPHYNX: an accurate density-based SPH method for astrophysical applications
- Improved Performances in Subsonic Flows of an SPH Scheme with Gradients Estimated using an Integral Approach
- Conservative, density-based smoothed particle hydrodynamics with improved partition of the unity and better estimation of gradients
- Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels
- WVTICs -- SPH initial conditions for everyone