SPH without a Tensile Instability

By Joseph J Monaghan. 2000

932 citations recorded by the source corpus.

Subfields: Computational Mechanics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fb2d80f6d3336ca8baf90719276362039db7be07

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In Computational Mechanics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Slope stability analysis using smoothed particle hydrodynamics (SPH) method (2015, neutral): “∂Wαβ ∂xj þFαi ð14Þ where Cij is the sum of the artificial viscosity term (Monaghan and Gingold, 1983) and the artificial stress term (Monaghan, 2000; Gray et al., 2001): Cαβij ¼ δijΠiþ RαijþRβij f αβ nAS ð15Þ where δij is Kronecker’s delta, ∏i is the artificial viscosity, Rαij and Rβij are the…”
Smoothed Particle Magnetohydrodynamics – II. Variational principles and variable smoothing-length terms (2003, methodology): “We resolve this instability by adding a short-range repulsive force to prevent particles from clumping (Monaghan 2000), the implementation of which is described in paper I.”
A robust weakly compressible SPH method and its comparison with an incompressible SPH (2012, methodology): “In passing, it should be mentioned that within the scope of this work, the artificial stress method [35, 36] has also been considered and implemented”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, background): “Morris (2000) showed several possible implementations of CSFmodel in SPH, both with and without exact conservation ofmomentum, andhighlighted the challenges in accurate calculations of interface curvature.”
Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves (2012, methodology): “Including the tensile instability correction, the modified concentration gradient is then rCi X j V jð1þ fijÞrxij: ð24Þ Experiments have shown that this modification with the values suggested by Monaghan [18] (R = 0.2, n = 4) works well.”
Boundary conditions generated by dynamic particles in SPH methods (2007, methodology): “Due to the particular choice of the cubic spline kernel, whose first derivative goes to cero with q, the tensile instability correction proposed by Monaghan (2000) was used to prevent particle clumping.”
A particle-based model for the transport of erythrocytes in capillaries (2009, methodology): “The line and arrow styles distinguish pairs of forces used to replace the bending moment on each line segment. instability by using the scheme of Monaghan (1994), which introduces a small repulsive force between nearby particles when they are in a state of tensile stress.”
Position based fluids (2013, methodology): “We follow the approach of [Monaghan 2000] which adds an artificial pressure specified in terms of the smoothing kernel itself as”
An MHD gadget for cosmological simulations (2008, background): “Monaghan (2000) suggested the introduction of an additional term in the momentum equation which prevents particles from clumping in the presence of strong magnetic stress.”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, background): “In particular Monaghan [61] suggested explicitly adding a short range repulsive force between particles to counteract the unphysical attractive force, similar to what would occur in atoms.”
Smoothed Particle Hydrodynamics in Astrophysics (2010, background): “Monaghan (2000) proposed instead an additional artificial pressure,which has the advantage of maintaining the conservative properties of SPH, but it introduces some small error in the dispersion relation.”
A stabilized Smoothed Particle Hydrodynamics, Taylor–Galerkin algorithm for soil dynamics problems (2013, background): “Later, Monaghan suggested applying an artificial force to control the tensile instability [48, 62].”