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diff --git a/typst/main.typ b/typst/main.typ new file mode 100644 index 0000000..198fd66 --- /dev/null +++ b/typst/main.typ @@ -0,0 +1,62 @@ +#import "@preview/charged-ieee:0.1.3": ieee + +#show: ieee.with( + title: [Stokes flow - Particle interaction in low Reynolds Number environments], + abstract: [ + ], + authors: ( + ( + name: "Claudius Holeksa", + department: [CSSR], + organization: [NORCE Research AS], + location: [Bergen, Norway], + email: "clho@norceresearch.no" + ), + ), + index-terms: ("Scientific writing", "Typesetting", "Document creation", "Syntax"), + bibliography: bibliography("refs.bib"), + figure-supplement: [Fig.], +) + += Introduction + +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, +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 + + +== 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 with Stokes flow + +So while + +// References +== References |
