Computational geometric methods for preferential clustering of particle suspensions

• Published in: Journal of computational physics Vol. 448; p. 110725
• Main Authors: Tapley, Benjamin K, Andersson, Helge I, Celledoni, Elena, Owren, Brynjulf
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.01.2022; Elsevier Science Ltd
• Subjects: Anisotropic particles; Clustering; Computational physics; Divergence; Exact solutions; Interpolation; Numerical analysis; Numerical methods; Particle-laden flows; Radial basis function; Radial basis functions; Semi-Lagrangian; Splitting methods; Velocity distribution; Particle-laden flows; Radial basis functions; Splitting methods; Anisotropic particles; Semi-Lagrangian
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110725

•An efficient geometric method better calculates preferential concentration of particles.•A contractivity-preserving splitting method preserves the sum of the Lyapunov spectrum.•The centrifuge effect is also mimicked in the numerical solution.•Non-divergence-free interpolation can erroneously cluster particles.•Matrix-valued RBFs are equivalent to interpolation via regularized Stokeslets. A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field with a splitting method integrator that preserves the sum of the Lyapunov spectrum while mimicking the centrifuge effect of the exact solution. We discuss how breaking the divergence-free condition in the interpolation step can erroneously affect how the volume of the particulate phase evolves under numerical methods. The methods are tested on suspensions of 104 particles evolving in a discrete cellular flow field. The results are that the proposed geometric methods generate more accurate and cost-effective particle distributions compared to conventional methods.