progress

2 files changed, 43 insertions, 8 deletions

diff --git a/typst/main.typ b/typst/main.typ
index d844d06..eb9f708 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -177,7 +177,8 @@ By sieving, bridging and aggregation of surface deposition.
 The least interesting phenomenon is sieving which results purely from a single particle having a too large of a volume to fit into the
 pore. While bridiging occurs when multiple particles arrive at a passage at the exact time, forming a stable arch which blocks the flow.  
 Aggregation involves the deposition of particles gradually  narrowing the channel.
-And while sieving and bridging results from purely mechanical forces aggregation results from electrostatic interactions between particles, the fluid and surface boundaries at micrometer scales@laurez2025bridging.
+And while sieving and bridging results from purely mechanical forces aggregation results from electrostatic interactions between particles in the fluid and surface boundaries at micrometer scales. In Laurez study@laurez2025bridging this
+effect is disregarded due to the scale of the problem and accumulation of particles occuring gradually.
 
 #figure(
 image("narrow_channel.png"),
@@ -189,6 +190,8 @@ caption: [One example geometry from Laurez@laurez2025bridging describing]
   caption: [Particles forming an arch visualized by Laurez@laurez2025bridging]
 )
 
+
+
 == Discusion
 
 The particles forming arches are often inherently unstable. Slight fluctuations in flow rate, local velocity gradients or the particle shape
@@ -196,13 +199,15 @@ can impact the particle arch formation and restore partial flow.
 But with the progression of aggregation arrive at less unstable states.
 Which in turn makes a stochastic analysis of particles in different conditions@laurez2025bridging based on different widths feasible.
 
-Laurez@laurez2025bridging goes into detail based on CITE FIG how probable clogging mechanisms are, while these are quite indepth, opportunities
-in relation to multiphase fluid interaction with the solid structures arise.
-Another interesting case is a variation in inbound pressure as usually the experimental setup 
+Laurez@laurez2025bridging goes into detail how probable clogging mechanisms are, while these are quite in depth, opportunities
+in relation to multiphase fluid interaction with the solid structures arise as well since his work focuses on a single phase fluid.
+Another interesting question is a variation in the inbound boundary pressure condition as Laurez looks into a constant inbound pressure
+while also mentioning that variability is introduced into the structures.
+Similar gaps can be seen in the other clogging mechanisms which might provide additional research targets.
 
 // Insert png
 
-== Lattice-Boltzmann-Method
+== Lattice-Boltzmann-Method in an overview
 
 Direct numerical simulation of creeping flow around many interacting particles in realistic porous structures is computationally challenging using
 conventional CFD methods.
@@ -215,9 +220,8 @@ image("d3q27.jpg"),
 caption: [An example of a discrete 27 velocity descriptor.]
 )
 
-Due to the fact that Lattice
 Through these stochastic behaviours, the macroscopic quantities such as velocity and pressure emerge naturally, recovering the Stokes flow
-or Navier-Stokes flow.
+or Navier-Stokes flow with one caveat, the incompressibility is not fully recovered and is thus weakly compressible.
 
 LBM is particularly suitable for simulating flow in complex porous geometries, because boundary conditions can be implemented directly at the
 cell level, making it ideal for digital rock simulations and is often employed in various fields.
@@ -225,4 +229,7 @@ The equisdistant grid and the properties of a cellular automaton make it a prime
 dependencies @krueger2017lbm.
 
 To couple a particle dynamics system two major approaches exist within Lattice Boltzmann.
-The immersed boundary method and the homogenized Lattice-Boltzmann-Method.
+The Immersed Boundary Method(IBM)@Peskin_2002 and the Homogenized Lattice-Boltzmann-Method(HLBM)@KRAUSE2017HLBM.
+The IBM approach is managed by calculating the coupling based on Lagrangian nodes from the point of view of the particles,
+requiring the recovery of the macroscopic variables and also distributing the force back.
+While the approach by HLBM incorporates most the of the 
diff --git a/typst/refs.bib b/typst/refs.bib
index cd30cd0..ec46a23 100644
--- a/typst/refs.bib
+++ b/typst/refs.bib
@@ -130,3 +130,31 @@ Wandeffekte in Betracht zieht.}
   year = 2017
 }
 
+@article{KRAUSE2017HLBM,
+title = {Particle flow simulations with homogenised lattice Boltzmann methods},
+journal = {Particuology},
+volume = {34},
+pages = {1-13},
+year = {2017},
+issn = {1674-2001},
+doi = {https://doi.org/10.1016/j.partic.2016.11.001},
+url = {https://www.sciencedirect.com/science/article/pii/S167420011730041X},
+author = {Mathias J. Krause and Fabian Klemens and Thomas Henn and Robin Trunk and
+Hermann Nirschl},
+keywords = {Particulate flow simulations, Arbitrarily shaped particles, Lattice Boltzmann
+methods, Validation, Sedimentation processes},
+abstract = {An alternative approach to simulating arbitrarily shaped particles submersed in
+viscous fluid in two dimensions is proposed, obtained by adapting the velocity parameter of
+the equilibrium distribution function of a standard lattice Boltzmann method (LBM).
+Comparisons of exemplifying simulations to results in the literature validate the approach as
+well as the convergence analysis. Pressure fluctuations occurring in Ladd’s approach are
+greatly reduced. In comparison with the immersed boundary method, this approach does
+not require cost intensive interpolations. The parallel efficiency of LBM is retained. An
+intrinsic momentum transfer is observed during particle–particle collisions. To demonstrate
+the capabilities of the approach, sedimentation of particles of several shapes is simulated
+despite omitting an explicit particle collision model.}
+}
+
+@article{Peskin_2002, title={The immersed boundary method}, volume={11},
+DOI={10.1017/S0962492902000077}, journal={Acta Numerica}, author={Peskin, Charles
+S.}, year={2002}, pages={479–517}}