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Diffstat (limited to 'typst')
| -rw-r--r-- | typst/report.typ | 20 |
1 files changed, 16 insertions, 4 deletions
diff --git a/typst/report.typ b/typst/report.typ index 8f16f96..112ed12 100644 --- a/typst/report.typ +++ b/typst/report.typ @@ -17,25 +17,37 @@ For the understanding of near-well injections multiple elements such as multipha 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 very viscous cases with our Reynolds number (Re \< \< 1) our base equation reduces itself to the Stokes Equations, 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 +todo insert NS eqs here are reduced to -@todo insert S eqs here +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 == Navier +The Navier Stokes equations are governed as follows + +// we don't really need the external force here? do we? + +#math.equation( +block: true, +$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\ +∇ · u = 0 $ +) + // Introduction == Stokes flow +While we are often interested in Navier-Stokes flows, on higher viscous fluids the viscosity dominates. + -== Solid-Fluid interaction +== Solid-Fluid interaction with Stokes flow So while |