# Simulating Stokes flow with an obstacle

I was asked to compute the Stokes flow (i.e. a low Reynolds fluid) near and obstacle. This is the first time I face a fluid and I am lost. What reference/general ideas/big theorems can you recommend me?

More details: given and obstacle (lets say, a bounded simply connected region $D\subset\mathbb{R}^2$ with $C^\infty$ boundary and all necessary stuff) and a steady flow $W\hat{x}$ from $-\infty\hat{x}$, I want to calculate the resultanting Stokes flow near $D$. For $D=\text{circle}$, the solution is well known (see, for example, page 4: http://web.mit.edu/2.21/www/Lec-notes/chap2_slow/2-5Stokes.pdf). In this reference, the formulas are derived from the continuity equation $\nabla\cdot q =0$ with boundary conditions $\text{at infinity}$. My idea was to use this approach, but I don't even know if it is possible to solve numerically a PDE with this kind of boundary conditions.

Thanks!

• This question is pretty confusing. (Though I am a big Better off Ted fan.) The first tool I'd recommend for flow around arbitrary objects might be the method of Regularized Stokeslets - this is very simple to code, and well-explained in Cortez et al. 2005, doi.org/10.1063/1.1830486 and the original Cortez paper (cited in that) – AJK Jan 5 '18 at 3:42
• You can't, in general, numerically solve problems that are posed on an infinite domain. But you can solve on a sequence or larger and larger domains, and then extrapolate the result to an infinite domain. – Wolfgang Bangerth Jan 7 '18 at 22:41