An immersed boundary method with direct forcing for the simulation of particulate flows

By Markus Uhlmann. 2005

1,707 citations recorded by the source corpus.

We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta Numerica 11 (2002) 1] into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations while at the same time avoiding strong restrictions of the time step. This technique was implemented in a finite-difference and fractional-step context. A variety of two- and three-dimensional simulations are presented, ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles. The accuracy and efficiency of the current method are clearly demonstrated.

Subfields: Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/a89bc70f63da8f9f1991b81f745bba80d0e5a232

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Ocean Engineering

Citations in the corpus

Pairwise interaction extended point-particle model for a random array of monodisperse spheres (2017, methodology): “The immersed boundary forcing f is calculated using the direct method introduced by Uhlmann (2005).”
Modulation of isotropic turbulence by particles of Taylor length-scale size (2010, methodology): “Uhlmann (2005) improved the IB method by minimizing the numerical oscillations resulting from the interaction forces between the fluid and the immersed solid body.”
Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction (2013, methodology): “The numerical method has been validated on a whole range of benchmark problems (Uhlmann, 2004, 2005a,b, 2006), and has been previously employed for the simulation of several flow configurations (Uhlmann, 2008; Chan-Braun, Garćıa-Villalba, and Uhlmann, 2011; GarćıaVillalba et al., 2012).”
A Sharp-Interface Immersed Boundary Method with Improved Mass Conservation and Reduced Spurious Pressure Oscillations (2011, methodology): “It is useful to point out that for diffuse-interface methods which include the discrete-delta function based implementation [7,8] or penalization based methods [14,15], the interface is normally described by a discretized delta function, which is spread smoothly over a set of local grid points.”
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations (2009, methodology): “In this case, the volume force needs to be evaluated through an interpolation at the Lagrangian markers using a discrete delta function, fðx; tnþ1=2Þ 1⁄4 XNl l1⁄41 FðX l ; tÞdhðx X nþ1 l ÞMVl: ð6Þ Here F is the force at the Lagrangian marker; Nl the total number of markers and MVl the volume assigne”
Lagrangian-Eulerian methods for multiphase flows (2013, background): “FRDNS of steady flow past fixed assemblies of monodisperse particles based on continuum Navier–Stokes equations (for example, the FR-DNS approach called Particle–resolved Uncontaminated–fluid Reconcilable Immersed Boundary Method (PUReIBM)) as well as the Lattice Boltzmann Method (LBM) have been use”
A comparative study of direct‐forcing immersed boundary‐lattice Boltzmann methods for stationary complex boundaries (2011, methodology): “Thus, for moving boundary problems, the diffuse interface scheme may be more desirable because it has a smooth change of forcing points [24] and its accuracy is reasonable within 5% compared with the sharp scheme as shown in the simulation of flow past a circular cylinder.”
Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids (2012, methodology): “The coupling of the fluid and the solid phase is realized by an IBM according to Uhlmann (2005) which is based on inserting additional volume forces in the vicinity of the interface.”
Flow patterns in the sedimentation of an elliptical particle (2009, methodology): “Uhlmann (2005) has extended the immersed boundary method (Lai & Peskin 2000; Mittal & Iaccarino 2005) to simulate flows with rigid particles.”