I am working on a fluid simulation using vortex methods. For this I must compute the vortex sheet on my boundaries given as: $$ \gamma(\mathbf{x}) - \frac{1}{\pi}\int_S \frac{\partial}{\partial\mathbf{n}}(\text{log}|\mathbf{x} - \mathbf{x'}|)\gamma(\mathbf{x'})d\mathbf{x'} = -2\mathbf{u}\cdot \mathbf{s} $$ I have two questions on how to compute the vortex sheet $\gamma$:

  1. The paper of Cooper and Barba state this can be solved using radial basis functions. I think the hardest part to compute is $$ \oint \frac{\partial}{\partial n}[\text{log}|\mathbf{x}-\mathbf{x'}|]\phi(|\mathbf{x'} - \mathbf{x_i}) d\mathbf{x'} $$ What would the discrete version of this be? So how do I compute this term?

  2. If I would use the panel method, how does a discretisation look like?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.