Smoothed Particle Hydrodynamics
Also known as: SPH, particle hydrodynamics
Smoothed Particle Hydrodynamics (SPH) is a meshfree particle method for simulating fluid dynamics, developed independently by Lucy in 1977 and Gingold and Monaghan in 1977. Rather than discretizing on a fixed grid, SPH represents fluids as collections of particles that carry mass, momentum, and energy. Each particle interacts with neighbors within a kernel support radius, enabling natural handling of free surfaces, large deformations, and multiphase flows without remeshing. SPH has become indispensable for simulations involving violent flows, impacts, and complex interfaces.
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When to use it
SPH excels for problems involving free surfaces, large deformations, impact dynamics, and multiphase flows. Use SPH for hydrocode simulations, asteroid collisions, tsunami propagation, and violent flow phenomena. Avoid SPH for steady flows where structured grids are more efficient, or for problems requiring extreme precision in smooth regions. SPH is less accurate than grid-based methods for thin boundary layers and requires careful tuning of kernel and smoothing length.
Strengths & limitations
- Natural handling of free surfaces without explicit interface tracking
- Excellent for extreme deformations, shattering, and topological changes
- Meshfree approach avoids remeshing and allows straightforward particle addition/removal
- Readily handles multiphase flows and fluid-structure interaction through particle mixing
- Naturally parallelizable; each particle's force computation depends only on neighbors
- Lower accuracy in smooth regions compared to finite-difference or finite-element methods of similar resolution
- Boundary condition implementation is non-trivial; wall effects require special treatment
- Kernel choice and smoothing length h significantly affect results; limited guidance on optimal values
- Computational cost scales as O(N log N) due to neighbor finding; can be expensive for large N
- Tensile instability in expanding flows can cause particle clustering and unphysical gaps
Frequently asked
What is the smoothing length h and how do I choose it?
The smoothing length h defines the radius of support for the kernel function—the region within which particles interact. Typical choice is h = 1.2 × particle spacing. Smaller h gives sharper features but increases cost and can cause particle clustering. Larger h smooths features and stabilizes the solution but reduces accuracy. Perform convergence studies: run at h, h/1.2, and h/1.5 and check when results stop changing.
What is artificial viscosity and why do I need it?
SPH can develop pressure oscillations across shocks (discontinuities in density/velocity). Artificial viscosity acts like a shock-capturing dissipation, smoothing these oscillations. Without it, solutions oscillate wildly. With too much, all flow features blur. Tuning parameters (typically α = 1, β = 2) requires experimentation. Modern variants (XSPH, delta-SPH) reduce artificial viscosity while maintaining stability.
How do I handle boundary conditions in SPH?
Boundaries are typically represented by fixed (or moving) boundary particles that exert repulsive forces on fluid particles. Alternatively, ghost particles mirror fluid particles across boundaries to enforce no-slip or symmetry conditions. Wall properties (roughness, permeability) are set at boundary particles. Treatment requires care to avoid unphysical density accumulation at walls.
What is tensile instability and how do I avoid it?
In regions with negative pressure (tension), particles may cluster uncontrollably, creating voids. This tensile instability is common in multiphase flows and free-surface flows near steep interfaces. Fixes include: adding surface tension models, using corrected kernels (CSPM), or applying particle shifting algorithms. Some codes use built-in stabilization that adjusts particle positions to prevent clustering.
How do SPH results compare to grid-based methods like RANS or LES?
SPH is typically less accurate for smooth, well-behaved flows but excels at violent transient phenomena. For a steady jet: RANS is more accurate. For a colliding dam: SPH captures the complex splashing better. The choice depends on whether smooth accuracy or complex dynamics is more important. Modern hybrid approaches couple SPH for free surfaces with Eulerian methods for bulk flow.
Sources
- Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82(12), 1013-1024. DOI: 10.1086/112164 ↗
- Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3), 375-389. DOI: 10.1093/mnras/181.3.375 ↗
- Monaghan, J. J. (2005). Smoothed particle hydrodynamics. Reports on Progress in Physics, 68(8), 1703-1759. DOI: 10.1088/0034-4885/68/8/R01 ↗
How to cite this page
ScholarGate. (2026, June 3). Smoothed Particle Hydrodynamics. ScholarGate. https://scholargate.app/en/fluid-dynamics/smoothed-particle-hydrodynamics
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