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| -rw-r--r-- | typst/main.typ | 11 |
1 files changed, 9 insertions, 2 deletions
diff --git a/typst/main.typ b/typst/main.typ index 9ca5a8c..136dc6c 100644 --- a/typst/main.typ +++ b/typst/main.typ @@ -58,15 +58,22 @@ velocity field $u(x,t)$ the Navier-Stokes formulation is primarly defined by the #math.equation( block: true, -$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f,\ +$ rho D/(Dt)u = ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f,\ ∇ · u = 0 $ ) +The left side represents the material derivative and thus the inerial acceleration, while the right side contains the pressure gradient, +viscous diffusion and potential body forces such as gravity. + While we are often interested in Navier-Stokes flows, a generalized analytical solution does not exist, most analytical approaches rely on a set of restrictions or assumptions. -With the Reynolds number defined by +One key parameter is the Reynolds number, previously mentioned before, defined as: + +#math.equation( +block: true, $ "Re" = (rho U L ) / mu $ +) Luckily we decided to work on a fluid which tends $"Re" arrow 0$ or at least $"Re" << 1$ where due to the viscous forces the inertial term is negligable and is assumed to be zero. |