Boundary condition handling, not just kernel choice, largely determines whether SPH simulations of Burgers' equation stay stable, and particles can cross through each other near boundaries when smoothing length far exceeds particle spacing.
From Petrov-Einstein to Navier-Stokes
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abstract
We consider a p+1-dimensional timelike hypersurface \Sigma_c embedded with a flat induced metric in a p+2-dimensional Einstein geometry. It is shown that imposing a Petrov type I condition on the geometry reduces the degrees of freedom in the extrinsic curvature of \Sigma_c to those of a fluid in \Sigma_c. Moreover, expanding around a limit in which the mean curvature of the embedding diverges, the leading-order Einstein constraint equations on \Sigma_c are shown to reduce to the non-linear incompressible Navier-Stokes equation for a fluid moving in \Sigma_c.
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physics.comp-ph 1years
2019 1verdicts
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On the boundary condition and related instability in the Smoothed Particle Hydrodynamics
Boundary condition handling, not just kernel choice, largely determines whether SPH simulations of Burgers' equation stay stable, and particles can cross through each other near boundaries when smoothing length far exceeds particle spacing.