A fictitious domain formulation for flows with rigid particles: a non-Lagrange multiplier version. (English) Zbl 1123.76069

Summary: We present a development of the fictitious domain method proposed in [C. Diaz-Goano, P. D. Minev, K. Nandakumar, J. Comput. Phys. 192, No. 1, 105–123 (2003; Zbl 1047.76042)]. The main new feature of the modified method is that after a proper splitting, it avoids the need to use Lagrange multipliers for imposition of the rigid body motion and instead, it resolves the interaction force between the two phases explicitly. Then, the end-of-step fluid velocity is a solution of an integral equation. The most straightforward way to resolve it is via an iteration but a direct extrapolation is also possible. If the latter approach is applied then the fictitious domain formulation becomes fully explicit with respect to the rigid body constraint and therefore, the corresponding numerical procedure is much cheaper. Most of the numerical results presented in this article are obtained with such an explicit formulation.


76T10 Liquid-gas two-phase flows, bubbly flows
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76M25 Other numerical methods (fluid mechanics) (MSC2010)


Zbl 1047.76042
Full Text: DOI


[1] Diaz-Goano, C.; Minev, P.; Nandakumar, K., A fictitious domain/finite element method for particulate flows, J. comput. phys., 192, 105, (2003) · Zbl 1047.76042
[2] Glowinski, R.; Pan, T.; Periaux, J., Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies, Comp. meth. appl. mech. eng., 151, 181, (1998) · Zbl 0916.76052
[3] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. multiphase flow, 25, 755, (1999) · Zbl 1137.76592
[4] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, 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. phys., 169, 363, (2001) · Zbl 1047.76097
[5] Patankar, N.; Singh, P.; Joseph, D.; Glowinski, R.; Pan, T., A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. multiphase flow, 26, 1509, (2000) · Zbl 1137.76712
[6] Pan, T.-W.; Glowinski, R., Direct simulation of the motion of neutrally buoyant circular cylinders in plane poiseuille’s flow, J. comp. phys., 181, 260, (2002) · Zbl 1178.76235
[7] Peskin, C., Numerical analysis of blood flow in the heart, J. comput. phys., 25, 220, (1977) · Zbl 0403.76100
[8] Patankar, N., A formulation for fast computations of rigid particulate flows, Center turbul. res., ann. res. briefs, 439, (2001)
[9] Sharma, N.; Patankar, N., A fast computation technique for the direct numerical simulation of rigid particulate flows, J. comp. phys., 205, 439, (2005) · Zbl 1087.76533
[10] Guermond, J.; Minev, P., Analysis of a projection/characteristic scheme for incompressible flow, Comm. numer. meth. engng., 19, 535, (2003) · Zbl 1112.76389
[11] Minev, P.; Ethier, C., A semi-implicit projection algorithm for the navier – stokes equations with application to flows in complex geometries, Notes on numerical fluid mechanics, 73, 223, (1999) · Zbl 1004.76061
[12] Veeramani, C.; Minev, P.; Nandakumar, K., A fictitious domain method for particle sedimentation, Lecture notes in comp. sci., 3743, 544, (2005) · Zbl 1142.76444
[13] ten Cate, A.; Nieuwstad, C.; Derksen, J.; den Akker, H.V., Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. fluids, 14, 4012, (2002) · Zbl 1185.76073
[14] Segré, G.; Silberberg, A., Radial particle displacements in poiseuille’s flow of suspensions, Nature, 189, 209, (1961)
[15] Pan, T.-W.; Glowinski, R., Direct simulation of the motion of neutrally buoyant balls in a three-dimensional poiseuille’s flow, C.R. mecanique, 333, 884, (2005) · Zbl 1173.76431
[16] Yang, B.; Wang, J.; Joseph, D.; Hu, H.; Pan, T.; Glowinski, R., Migration of a sphere in a tube flow, J. fluid mech., 540, 109, (2005) · Zbl 1082.76028
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