# zbMATH — the first resource for mathematics

Spectral element simulations of interactive particles in a fluid. (English) Zbl 1442.76127
Summary: This paper presents three-dimensional simulations of interactive particles in a fluid. The originality of this paper is the integrated Eulerian-Lagrangian algorithms implemented with high-order methods in both space and time for numerical solutions to Navier-Stokes equations with additional source terms. Implementation of fourth order Stiffly Stable Schemes was tested for time integration before they were used in computations. In order to provide the $$hp$$-type mesh refinement, for extra flexibility to achieve higher spatial resolution, a modal spectral element method was used to solve governing equations in three dimensions. Another originality is the efficiency in handling moving particles without adaptive or moving mesh. Simulation results were validated with experimental data and verified with exact solutions. In addition, numerical results were also compared with solutions at higher resolutions and good agreement was accomplished. Results indicate that algorithms and implementations are accurate and appropriate for investigating three dimensional interactive particles in a fluid involving many moving objects.
##### MSC:
 76T20 Suspensions 76D05 Navier-Stokes equations for incompressible viscous fluids 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Peano
Full Text: