# zbMATH — the first resource for mathematics

An efficient multigrid-FEM method for the simulation of solid-liquid two-phase flows. (English) Zbl 1110.76032
Summary: We present an efficient multigrid-FEM method for detailed simulation of solid-liquid two-phase flows with large number of moving particles. An explicit fictitious boundary method based on a FEM background grid which covers the whole computational domain and can be chosen independently from the particles of arbitrary shape, size and number is used to deal with the interactions between the fluid and the particles. Since the presented method treats the fluid part, the calculation of forces and motion of particles in a subsequent manner, it is potentially powerful to efficiently simulate real particulate flows with huge number of particles. The presented method is first validated using a series of simple test cases, and then, as an illustration, we present simulations of three big disks plunging into 2000 small particles, and of sedimentation of 10,000 particles in a cavity.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76T20 Suspensions 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
##### Keywords:
fictitious boundary method; particulate flow
FEATFLOW
Full Text:
##### References:
 [1] Diaz-Goano, C.; Minev, P.D.; Nandakumar, K., A fictitious domain/finite element method for particulate flows, J. comput. phys., 192, 105-123, (2003) · Zbl 1047.76042 [2] Duchanoy, C.; Jongen, T.R.G., Efficient simulation of liquid – solid flows with high solids fraction in complex geometries, Comput. and fluids, 32, 1453-1471, (2003) · Zbl 1128.76336 [3] Feng, Z.G.; Efstathios, E., Michaelides: proteus: a direct forcing method in the simulations of particulate flows, J. comput. phys., 202, 20-51, (2005) · Zbl 1076.76568 [4] Glowinski, R., Numerical methods for fluids (part 3), () · Zbl 0612.76033 [5] Glowinski, R.; Pan, T.W.; Hesla, T.I.; Joseph, D.D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Internat. J. multiphase flow, 25, 755-794, (1999) · Zbl 1137.76592 [6] Glowinski, R.; Pan, T.W.; Hesla, T.I.; Joseph, D.D.; Periaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J. comput. phy., 169, 363-426, (2001) · Zbl 1047.76097 [7] Hu, H.H., Direct simulation of flows of solid – liquid mixtures, Internat. J. multiphase flow, 22, 335-352, (1996) · Zbl 1135.76442 [8] Hu, H.H.; Joseph, D.D.; Crochet, M.J., Direct simulation of fluid particle motions, Theoret. comput. fluid dyn., 3, 285-306, (1992) · Zbl 0754.76054 [9] Hu, H.H.; Patankar, N.A.; Zhu, M.Y., Direct numerical simulations of fluid – solid systems using the arbitrary lagrangian – eulerian techniques, J. comput. phys., 169, 427, (2001) · Zbl 1047.76571 [10] Johnson, A.A.; Tezduyar, T.E., Simulation of multiple spheres falling in a liquid-filled tube, Comput. methods appl. mech. engrg., 134, 351-373, (1996) · Zbl 0895.76046 [11] D.D. Joseph, R. Glowinski, H.H. Hu, Y. Saad, V. Sarin, P. Singh, Direct simulation of the motion of particles in flowing liquids, A proposal to NSF KDI/New Computational Challenge.(1998-2001). [12] Ladd, A.J.C., Numerical simulation of particulate suspensions via a discretized Boltzmann equation. I. theoretical foundation, J. fluid mech., 271, 285-309, (1994) · Zbl 0815.76085 [13] Ladd, A.J.C., Numerical simulation of particulate suspensions via a discretized Boltzmann equation. II. numerical results, J. fluid mech., 271, 331-339, (1994) · Zbl 0815.76085 [14] Ladd, A.J.C.; Verberg, R., Lattice-Boltzmann simulations of particle fluid suspensions, J. statist. phys., 104, 1191, (2001) · Zbl 1046.76037 [15] Maury, B., Characteristics ALE method for the unsteady 3D navier – stokes with a free surface, Internat. J. comput. fluid dynamics, 6, 175-188, (1996) [16] Maury, B., Direct simulations of 2D fluid-particle flows in biperiodic domains, J. comput. phy., 156, 325-351, (1999) · Zbl 0958.76045 [17] Patankar, N.A.; Singh, P.; Joseph, D.D.; Glowinski, R.; Pan, T.W., A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Internat. J. multiphase flow, 26, 1509-1524, (2000) · Zbl 1137.76712 [18] M. Schäfer, S. Turek, Benchmark computations of laminar flow around cylinder, in: E.H. Hirschel (Ed.), Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics, vol. 52, Vieweg, 1996. p. 547. [19] Singh, P.; Hesla, T.I.; Joseph, D.D., Distributed Lagrange multiplier method for particulate flows with collisions, Internat J. multiphase flow, 29, 495-509, (2003) · Zbl 1136.76643 [20] Turek, S., A comparative study of time stepping techniques for the incompressible navier – stokes equations: from fully implicit nonlinear schemes to semi-implicit projection methods, Internat. J. numer. methods fluids, 22, 987-1011, (1996) · Zbl 0864.76052 [21] Turek, S., On discrete projection methods for the incompressible navier – stokes equations: an algorithmical approach, Comput. methods appl. mech. engrg., 143, 271-288, (1997) · Zbl 0898.76069 [22] Turek, S., FEATFLOW—finite element software for the incompressible navier – stokes equations: user manual, release 1.1, (1998), University of Heidelberg [23] Turek, S., Efficient solvers for incompressible flow problems, (1999), Springer Berlin, Heidelberg, New York [24] S. Turek, D.C. Wan, L.S. Rivkind, The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations, Challenges in Scientific Computing, Lecture Notes in Computational Science and Engineering, vol. 35, Springer, Berlin, 2003, 37-68. · Zbl 1138.76388 [25] D.C. Wan, S. Turek, Direct Numerical Simulation of Particulate Flow via Multigrid FEM Techniques and the Fictitious Boundary Method, Ergebnisbericht Nr. 275, Fachbereich Mathematik LS III, Universit$$\ddot{\operatorname{a}}$$t Dortmund, (2004). Internat. J. Numer. Methods Fluid, 51 (2006) 531-566. · Zbl 1145.76406 [26] D.C. Wan, S. Turek, L.S. Rivkind, An efficient multigrid FEM solution technique for incompressible flow with moving rigid bodies, Numerical Mathematics and Advanced Applications, ENUMATH 2003, Springer, Berlin, 2004, pp. 844-853. · Zbl 1216.76037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.