progress

1 files changed, 29 insertions, 14 deletions

diff --git a/typst/main.typ b/typst/main.typ
index 198fd66..ed1d4b9 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -20,27 +20,26 @@
 
 = Introduction
 
+Flow in porous subsurface structures often is dominated by low velocity and high viscous fluids with low Reynolds numbers,
+often referred to as Stokes flow or creeping flow.
+It occurs when the viscous forces are significantly larger compared to inertial forces.
+
 For the understanding of near-well injections multiple elements such as multiphase behaviour, particle-solid interaction and
 the geometry of the porous structure is required.  
 While at heart most numerical modelling approaches such as the Lattice-Boltzmann-Method are based on the Navier-Stokes Equations,
 here we will take a glance on a more special case.  
-Since we are interested in very viscous cases with our Reynolds number (Re \< \< 1) our base equation reduces itself to the Stokes Equations,
+Since we are interested in low velocity and high viscous cases the Reynolds number (Re \< \< 1) of our base equation reduces itself to
+the Stokes Equations due to the relation $Re=U*v/L$,
 which are well understand in terms of the description by Stokes [dummy, I mean the old paper from 1851].
-So the Navier-Stokes equations
-
-todo insert NS eqs here
-
-are reduced to
-
-todo insert S eqs here
-// Rather move this to the lower chapters and use book citations I guess. Well, maybe also Stokes paper. The initial rant is quite fun
+So starting from the incompressible Navier-Stokes equations we will assume a mostly laminar flow such that the inertial effects
+are not considered, but are dominated by the viscous forces.
 
+Viscous flows are often 
 
 == Navier
 
-The Navier Stokes equations are governed as follows
-
-// we don't really need the external force here? do we?
+// Write about Navier
+The incompressible Navier Stokes equations are a set of equations
 
 #math.equation(
 block: true,
@@ -51,12 +50,28 @@ $ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\
 // Introduction
 == Stokes flow
 
-While we are often interested in Navier-Stokes flows, on higher viscous fluids the viscosity dominates.
+While we are often interested in Navier-Stokes flows, on higher viscous fluid such as in the earth's mantle the inertial term is negligable.
+Since we 
+
+// Stokes
+#math.equation(
+block: true,
+$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\
+∇ · u = 0 $
+)
 
 
 == Solid-Fluid interaction with Stokes flow
 
-So while
+Since 
+// Boundary
+//
+
+
+// Different boundary examples ?
+
+
+
 
 // References
 == References