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

An adaptive approach to remove tensile instability in SPH for weakly compressible fluids