The heart of the problem is a mismatch of scales. The Discrete Element Method, or DEM, has become the workhorse of computational granular physics since its development by Peter Cundall in 1971 and its landmark extension with Otto Strack in 1979. DEM applies Newton’s second law of motion to the centre of every particle and a force-displacement law at every contact, computing the trajectory of each grain through time. Collisions are typically modelled as viscoelastic spring-dashpot systems, capturing both the repulsive force and the dissipated kinetic energy. Coupled with Computational Fluid Dynamics in the early 1990s, DEM-CFD can now simulate landslides, debris flows, pyroclastic currents, riverbed transport and industrial powder handling with remarkable fidelity. But what the simulations deliver is a torrent of particle-scale data: individual velocities, individual forces, individual contacts. Science and engineering, however, speak the language of continuum fields such as pressure, stress, strain rate and density.

Bridging that gap requires a mathematical procedure known as coarse-graining, a discrete-to-continuum transformation in which macroscopic fields emerge as spatially weighted averages of microscopic quantities. Each particle contributes to the field at a given point according to a weighting function that spreads its influence over a small volume, effectively smearing the point-like mass of the particle into a smooth density. Crucially, the method makes no assumption that particles are spherical or rigid, and it works across flow regimes from solid-like quasi-static behaviour to fluid-like rapid flow. The theoretical foundations trace back to Babic’s 1997 averaging framework for granular media, itself inspired by spatio-temporal weighted averaging in molecular dynamics, and have been refined over decades to handle boundaries, scale dependence and polydisperse mixtures.

Despite this maturity, the software ecosystem has lagged. Some DEM packages, such as LAMMPS and MercuryDPM, include built-in coarse-graining capabilities. Others, notably the open-source MFiX-DEM developed by the United States National Energy Technology Laboratory, do not, forcing users to write custom post-processing code or contort their simulation outputs to fit other tools. That fragmentation, the Edinburgh team argues, hampers reproducibility and invites error propagation. Pysammos, whose name nods to Archimedes’ The Sand Reckoner and his attempt to count the grains of sand that could fill the universe, was built to fill this void: a user-friendly, computationally efficient Python package that reads MFiX-DEM output directly and produces continuum fields ready for analysis and visualisation.

Technically, the package implements the full weighted-average machinery. It computes the mass density, momentum density and velocity fields, and it evaluates the stress tensor as the sum of a contact part and a kinetic part. Contact forces are distributed along the branch vector connecting two touching particles through a line integral of the weighting function, which Pysammos evaluates numerically with a trapezoidal rule that the authors show is already converged with just ten sampling points. Users can choose among three smoothing kernels: the Lucy polynomial, a cut-off Gaussian and a Heaviside step function. The authors recommend the Lucy function, because the Heaviside kernel weights all particles in the averaging volume equally and thereby amplifies edge effects, while the truncated Gaussian technically violates the differentiability required for the continuum balance equations to hold exactly.

The choice of smoothing width, the resolution at which the continuum fields are computed, turns out to be anything but trivial. The kinetic stress tensor is intrinsically dependent on the square of the averaging width, because it captures velocity gradients between a particle’s position and the evaluation point. Previous work has identified two length scales at which coarse-grained fields become nearly independent of the averaging width: one below the particle scale, which can resolve thin flow layers near boundaries, and one at the particle scale, which yields smooth fields. Pysammos adopts a default smoothing width of 0.75 times a representative particle diameter, but the team stresses that users should verify the stability of their results for their particular flow regime.

One of the package’s most distinctive features is its automated phase detection. In polydisperse mixtures, particles segregate by size and density through competing mechanisms known as kinetic sieving and buoyancy. Pysammos clusters the particle data by diameter and density using the k-means algorithm, selecting the optimal number of phases via silhouette analysis, and then computes partial continuum fields for each phase separately. Mixture theory then superposes these partial fields to recover the bulk behaviour. The team demonstrated this on a simulated granular pile confined between walls, revealing the classic stress-arching phenomenon: instead of the hydrostatic pressure maximum a fluid would show beneath the pile’s peak, the basal pressure exhibits a local minimum because force chains redirect the weight sideways toward the flanks.

The showcase applications span the geosciences. A bedload transport simulation of polydisperse, non-spherical grains under travelling water waves revealed bands of elevated shear rate and inertial number at the wave fronts, invisible in the raw contact network. A high-speed impact on a million-particle granular bed, relevant to cratering on asteroids and seismology alike, showed a downward-propagating shock wave and a friction coefficient exceeding the static value around the impact zone. A pseudo-2D simulation of crystals suspended in magma flowing through a conduit quantified how the effective shear viscosity varies with wall friction. And an erodible-bed experiment reproduced the classic Bagnold velocity profile, with granular temperature increasing toward the base where grains rattle against a rough floor.

Benchmarking against established coarse-graining software, including MercuryCG, EDEM’s continuum analysis, Granulysed and Iota-Suite, showed that Pysammos reproduces the expected fields, with results from its Gaussian and Lucy kernels coinciding closely with MercuryCG’s weighted averaging scheme. Performance tests on the ARCHER2 supercomputer showed that the cost per particle decreases sub-linearly with system size, meaning overheads are amortised and caches are used efficiently. Efficient execution does not demand massive parallel resources: at sub-particle resolution a couple of cores suffice, while large dense packings at coarser resolution benefit from four to sixteen cores. That makes the tool practical on ordinary desktop machines as well as high-performance clusters, lowering the barrier for research groups without dedicated computing infrastructure.

The team positions Pysammos as a contribution to a broader effort to standardise and streamline DEM post-processing across an inherently interdisciplinary community spanning geosciences, engineering and physics. Future versions are planned to read data from other DEM packages such as LAMMPS and YADE, to offer more flexible meshing beyond the current structured cuboid grid, and to account for the effect of hard boundaries on the contact stress tensor. Work is also under way with the MFiX developers to enable rigorous coarse-graining of glued-sphere particles, which approximate irregular shapes such as angular volcanic ash. For a field in which the second-most-handled material by weight in global industry, behind only water, still defies a unified description, a well-documented, open-source bridge from grain to continuum may prove a quietly transformative piece of infrastructure.

Subject of Research: A discrete-to-continuum coarse-graining software tool for analysing the rheology of granular materials from DEM simulations

Article Title: Pysammos 1.0.0: a discrete-to-continuum transformation Python tool to analyse the rheology of granular materials

Article References: Pysammos 1.0.0: a discrete-to-continuum transformation Python tool to analyse the rheology of granular materials. (n.d.). https://doi.org/10.5194/gmd-19-9519-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9519-2026

Keywords: granular flows, Pysammos, Discrete Element Method, coarse-graining, rheology, DEM-CFD, MFiX, geohazards, sediment transport, open-source software, computational physics, continuum mechanics

A new study published in Ocean Dynamics by Feidong Zheng of PowerChina Kunming Engineering Corporation Limited and colleagues, including researchers at Nanjing Hydraulic Research Institute and Nanjing University of Information Science and Technology, now offers a predictive framework that spans the full spectrum of wave energy. The work extends the team’s earlier high-energy investigations with a fresh set of controlled laboratory experiments focused specifically on low-energy responses, allowing the researchers to stitch the two regimes into one coherent model. The result is a suite of equations that predicts not only how tall the waves will be, but how they attenuate with distance, how their periods and wavelengths evolve through dispersion, and how the energy of the collapsing granular mass is transferred into the water.

The physics of the problem is deceptively intricate. A subaerial granular landslide is not a rigid block; it is a porous, deformable collection of grains that disintegrates as it slides, impacts the free surface, and continues to move underwater. The wave that emerges depends on the slide’s volume, velocity, thickness, and impact angle, as well as the water depth and the geometry of the reservoir. Classical approaches, such as the widely used model of Heller and Hager developed at ETH Zurich, condense these variables into an impulse product parameter that captures the strength of the landslide impact. That framework has proven robust for the largest, most energetic waves, but its performance for gentler, Stokes-like waves, in which the free surface oscillates in a nonlinear but still wave-like fashion, had not been systematically tested.

Zheng and his co-authors began by doing exactly that: validating the Heller and Hager model against their new low-energy data across the entire energy spectrum. The model held up remarkably well. For maximum wave height, the mean deviation between prediction and measurement was about 15 percent, a figure the authors describe as confirming the reliability of the classical formulation from the weakest oscillatory responses up to the most violent surges. In practical terms, this means engineers can continue to use the established height model with confidence, knowing it does not silently fail when a landslide is smaller or slower than the laboratory benchmarks on which it was originally calibrated.

But wave height alone does not tell the whole hazard story. The maximum amplitude, the single highest excursion of the water surface above still-water level, is often the quantity that determines whether a wave overtops a dam or floods a shoreline bench. Here the team went beyond validation and derived a novel maximum amplitude model of their own, and the improvement is striking: prediction errors fell to 7.80 percent, roughly half the deviation of the height model. The tighter fit is not merely a statistical achievement. The new equation is consistent with a specific physical interpretation of how Stokes-like waves are born, namely that the vertical, kinematic displacement of the free surface, driven by the slide pushing water upward and outward at the impact zone, dictates amplitude generation, rather than the deep transfer of mass momentum through the water column.

That distinction matters because it changes how one thinks about the hazard. If amplitude were controlled by bulk momentum injected deep into the water, then the mass and submerged motion of the landslide would dominate, and mitigation strategies would focus on the underwater runout. If instead the kinematic free-surface displacement is the governing mechanism, as the new model suggests for Stokes-like regimes, then the geometry and speed of the slide at the moment it crosses the shoreline become the critical controls. The authors’ laboratory observations support the latter picture, giving hazard assessors a clearer target for the parameters that most influence the worst-case water-surface excursion near the impact site.

The framework does not stop at the wave crest. Zheng and colleagues developed type-specific governing equations for wave attenuation, describing how the impulse waves lose height as they propagate away from the impact zone, and for the dispersive evolution of wave period and wavelength, capturing how an initially impulsive disturbance stretches into a longer, more regular wave train as frequency components separate with distance. These propagation characteristics are essential for translating a near-field measurement or prediction into an estimate of what a wave will look like when it reaches a dam face or a lakeside community kilometers downstream. A wave that is modest at the source may still carry dangerous energy if its period lengthens in a way that resonates with the geometry of a narrow reservoir arm.

Perhaps the most conceptually interesting component is the team’s energy model, which captures what the authors call mass-dependent momentum coupling. In their experiments, the porous granular mass does not behave as an impermeable piston. Instead, water can percolate into and through the disintegrating slide, and the granular skeleton buffers the interaction between the solid and fluid phases. The model demonstrates physically how this buffering regulates the efficiency of energy transfer from the landslide to the water: a highly porous, rapidly disintegrating mass dissipates more of its kinetic energy internally and in grain-fluid friction, delivering less to the wave, while a denser, more coherent mass couples its momentum more effectively into the free surface. This provides a mechanistic explanation for why granular landslides of equal volume and speed can produce markedly different waves depending on their internal structure and grain-size distribution.

The experimental campaign behind these results sits within a broader body of work by the same group, which has previously examined impulse waves across a broad spectrum of grain diameters, waves generated by subaerial cylinders, and the influence of rigid vegetation on wave characterization, as well as numerical simulations using coupled smoothed particle hydrodynamics and discrete element methods. By anchoring the new low-energy experiments to that earlier high-energy dataset, the authors avoid the common pitfall of building a model that fits one regime beautifully and another not at all. The unified framework is explicitly empirically derived, meaning its coefficients come from measurement rather than assumption, yet each equation carries an explicit physical interpretation, a combination that should make it easier for practitioners to judge when the model can be extrapolated and when it cannot.

For reservoir operators and geohazard agencies, the practical payoff is a set of tools that can be applied across the full range of plausible landslide scenarios, from small rockfalls that generate gentle oscillations to large collapses that launch near-field surges. The research was supported by Yunnan Fundamental Research Projects, a POWERCHINA Science and Technology Project, and Yunnan’s Technology Innovation Center for Digital Water Engineering, reflecting the acute relevance of landslide-generated waves to the hydropower reservoirs of southwestern China, where steep terrain, seismicity, and monsoonal loading keep slopes in a state of perpetual tension with the water below. With validated height predictions, a high-accuracy amplitude model, propagation and dispersion equations, and an energy-transfer framework grounded in the physics of granular porosity, the study moves the field closer to the long-sought goal of a single, trustworthy forecast: given a landslide on the slope, how big will the wave be, how fast will it decay, and how much of the slide’s energy will the reservoir ultimately absorb.

Subject of Research: Predictive modeling of impulse waves generated by subaerial granular landslides in reservoirs

Article Title: Unified predictive framework for subaerial granular landslide-generated stokes-like waves across energy regimes

Article References: Zheng, F., Liu, Q., Xue, Z., Li, C., Yang, Y., Yao, C., Huang, T., Liu, G., Xu, J., & Lin, X. (2026). Unified predictive framework for subaerial granular landslide-generated stokes-like waves across energy regimes. Ocean Dynamics, 76(10), Article 104. https://doi.org/10.1007/s10236-026-01862-z

Image Credits: AI Generated

DOI: 10.1007/s10236-026-01862-z

Keywords: landslide-generated impulse waves, Stokes-like waves, subaerial landslides, reservoir geohazards, wave amplitude prediction, wave attenuation, energy conversion, granular flows, laboratory experiments, Heller and Hager model, Ocean Dynamics, hazard assessment