SPH (Smoothed Particle Hydrodynamics) is a particle, purely mesh-free Lagrangian method, proposed by different authors, well suited to the computing of highly transitory free surface flows of complex fluids in complex geometries. Different approaches have been proposed in order to better simulate the mutual interaction between particles and their interactions with boundaries.
Therefore, the main target of this article is to discuss and explore the numerical performance of certain commonly utilized SPH approaches, based essentially on mass and momentum balances, in the simulation of a 2D fast mudflow in fast motion, composed of fluid and solid material, assumed to be just one equivalent phase (fluid-solid). The “Herschel-Bulkley”, non Newtonian constitutive equations, describing a viscoplastic material suitable to reproduce the rheological behaviour of mudflows, has been selected. Hence, a laboratory experimental test, already proposed in literature and, after properly scaling, representative of a real fast flow phenomenon, was considered for comparison with numerical outcomes carried out by a research code that has already been tested and discussed in previous papers. A simple but effective statistical approach was developed and applied in order to identify and utilize a numerical index suitable for the quantitative measurement of the degree of matching between numerical results and measurement data affected by experimental errors. More than thirty numerical experiments were performed, of which the most significant eleven simulations are discussed. Satisfactory results were achieved. As outcomes, it was verified that, in particular for the selected experimental test, Rusanov flux addition within the continuity equation with the proper choice of both the viscosity term of momentum and the SPH boundary conditions, is suited to enhancing the performance of this type of numerical simulation of a fast flow.