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Dynamic boundary conditions (DBC) for solid surfaces are standard in the weakly compressible smoothed particle hydrodynamics (SPH) code DualSPHysics. A stationary solid is simply represented by fixed particles with pressure from the equation of state. Boundaries are easy to set up and computations are relatively stable and efficient, providing robust numerical simulation for complex geometries. However, a small unphysical gap between the fluid and solid boundaries can form, decreasing the accuracy of pressures measured on the boundary. A method is presented where the density of solid particles is obtained from ghost positions within the fluid domain by linear extrapolation. With this approach, the gap between fluid and boundary is reduced and pressures in still water converge to hydrostatic, including the case of a bed with a sharp corner. The violent free-surface cases of a sloshing tank and dam break impact on an obstacle show pressures measured directly on solid surfaces in close agreement with experiments. The complex 3-D flow in a fish pass, with baffles to divert the flow, is simulated showing close agreement with measured water levels with weirs open and gates closed, but less close with gates open and weirs closed. This indicates the method is suitable for rapidly varying free-surface flows, but development for complex turbulent flows is necessary. The code with the modified dynamic boundary condition (mDBC) is available in DualSPHysics to run on CPUs or GPUs.

New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time $t$; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

We present a theoretical and experimental analysis of axisymmetric gravity currents of power-law fluids in homogeneous porous media. The non-Newtonian shear-thinning fluid is a mixture of water, glycerol and Xanthan gum (n = 0.33-0.53), and it is injected into a porous layer of glass beads (d = 1-3 mm). We compare experiments conducted with constant (α = 1) and time-increasing (α = 1.5 and 2.0) influxes to theoretical self-similar solutions obtained by the numerical integration of the nonlinear ordinary differential equation that describes one-dimensional transient motion. The theoretical analysis is confirmed by experimental data. In addition, the selection of the most appropriate expression for the tortuosity factor and the choice of the correct range of shear stress for the determination of the rheological parameters are shown to be crucial to obtaining a good fit between the theory and experiments.