Multidomain BEM for laminar flow in complex fractal geometry

摘要

This paper demonstrates the highly efficient 2D multidomain Boundary Element Method (BEM) for solving stream functionvorticity equations on fractal geometry containing a thousand corners and a hundred recirculation zones. Considering the sharp corners, two problems are solved. The problem of undefined unit normal in corner is overridden using mixed boundary element discretisation. The second problem is on determining the boundary vorticity values used as a boundary condition in a vorticity transport equation for a no-slip boundary. The implicit computation of boundary vorticities from a stream function governing equation as an integral constraint is applied. The numerical example is an intricate fractal geometry of the Koch snowflake solved in a large variation of Reynolds number values ranging from 10(-6) to 100. The flow pattern self-similarity is obtained, equivalent to fractal geometry similarity.