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 $\gamma$: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?If I would use the panel method, how does a discretisation look like?
Discretizing boundary conditions for vortex methods
simulation;boundary conditions;fluid;vortex