![]() ![]() In the state of the art, convergence is typically between the first- and second-order theoretical limits. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. ![]() While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Now numerical convergence studies are standard. This was effectively removed in the incompressible (divergence-free) form which followed since then the weakly compressible form has been advanced, reducing pressure noise. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. ![]() As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. ![]()
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