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authorClaudius "keldu" Holeksa <mail@keldu.de>2025-11-11 09:49:36 +0100
committerClaudius "keldu" Holeksa <mail@keldu.de>2025-11-11 09:49:36 +0100
commitcdb177792a74856849149524dc31ff43bc2b650e (patch)
treecaffac6964cd10aa57f11e444937b49492cce5c0 /typst/report.typ
parentdebb75b90b5b37114e1282caa540790c5ac70638 (diff)
downloadphd-fluid_mechanics_report-cdb177792a74856849149524dc31ff43bc2b650e.tar.gz
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-// Title Page
-= Solid particle interaction in Stokes flow
-
-Author: "Claudius Holeksa"
-Date: 2025-11-09
-
-// Abstract
-// == Abstract
-// This is a brief summary of the report. It gives an overview of the objectives, methods, and conclusions.
-
-// Table of Contents
-[toc]
-
-== 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