  Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile
instability, which is the occurrence of short wavelength zero energy modes
resulting in unphysical clustering of particles. The root cause of the
instability is the shape of derivative of the compactly supported kernel
function which may yield negative stiffness in the particle interaction under
certain circumstances. In this work, an adaptive algorithm is developed to
remove tensile instability in SPH for weakly compressible fluids. Herein, a
B-spline function is used as the SPH kernel and the knots of the B-spline are
adapted to change the shape of the kernel, thereby satisfying the condition
associated with stability. The knot-shifting criterion is based on the particle
movement within the influence domain. This enables the prevention of
instability in fluid problems where excessive rearrangement of particle
positions occurs. A 1D dispersion analysis of an Oldroyd B fluid material model
is performed to show how the algorithm prevents instabilities for short
wavelengths but ensures accuracy at large wavelengths. The efficacy of the
approach is demonstrated through a few benchmark fluid dynamics simulations
where a visco-elastic Oldroyd B material model and a non-viscous Eulerian fluid
material model are considered.
