Robustness and accuracy of SPH formulations for viscous flow

Abstract

SUMMARYNumerous methods are available for the modelling of viscous stress terms in smoothed particle hydrodynamics (SPH). In this work, the existing methods are investigated systematically and evaluated for a range of Reynolds numbers using Poiseuille channel and lid-driven cavity test cases. The best results are obtained using two methods based on combinations of finite difference and SPH approximations, due to Morris et al. and Cleary. Gradients of high-valued functions are shown to be inaccurately estimated with standard SPH. A method that reduces the value of functions (in particular, pressure) before calculating the gradients reduces this inaccuracy and is shown to improve performance. A mode of instability in Poiseuille channel flows, also reported in other works, is examined and a qualitative explanation is proposed. The choice of boundary implementation is shown to have a significant effect on transient velocity profiles in start-up of the flow. The use of at least linear extrapolation for in-wall velocities is shown to be preferable to mirroring of velocities. Consistency corrections to the kernel are also found to result in significant accuracy and stability improvements with most methods, though not in all cases.

Momentum conserving Brownian dynamics propagator for complex soft matter fluids

“…The sum includes the term k = j. Basa et al 12 showed that Eq. (11) is the best among different available schemes in smoothed particle hydrodynamics for approximation of the second derivatives.…”

Permeable and non‐reflecting boundary conditions in SPH

“…Therefore, this formulation conserves linear and angular momentum. These properties are discussed more fully by Violeau and Issa [9] and Basa et al [10]. The term R ab f ab ∇W ab is Monaghan's interparticle force [11] defined by…”

“…Similarly, at the outflow boundary, J 1 and J 2 should be determined from the interior, while the boundary condition is J 3 = 0. By inverting the system of equations (10)(11)(12), it is straightforward to express pressure, density, and velocity as functions of the characteristic variables as shown below.…”

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

“…The truncation errors of the SPH discretization of spatial derivatives have been studied numerically in [31,32] and analytically in [18,33]. In SPH, particles move with the fluid velocity and become disordered in the nonuniform velocity field.…”