Complex geometry handling for a cartesian grid based solver

Abstract

Complex geometries can be a challenge for computational fluid dynamics (CFD) solvers that use a Cartesian mesh. In the current paper, an algorithm is described with which complex geometry features can be incorporated in a ghost cell immersed boundary method through a simple and straightforward algorithm. The complex geometries are handled with a trivial triangular surface mesh in the widely used STL format. Grid generation is than achieved with an optimized ray-tracing algorithm, which determines solid and fluid cells, as well as the closest distances from the solid boundaries to the neighboring fluid cells. As the numerical model uses a Cartesian mesh, the presence of irregular solid boundaries is handled by immersing them through ghost cell extrapolation into the fluid domain. The capabilities of the presented method are shown through two real-world examples: wave hydrodynamics around an offshore wind turbine jacket substructure and supercritical flow over the spillways of a hydropower plant. The numerical model used in this study is REEF3D, an open-source three-dimensional CFD code. It employs the level set method for the representation of the free surface. This approach is capable of handling complex air-water interface topologies. The ReynoldsAveraged Navier-Stokes (RANS) equations are discretized with the fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) scheme in space and with a third-order Runge-Kutta based fractional step scheme in time. For the pressure, the projection method is used on a staggered grid configuration, assuring tight pressure-velocity coupling. The model solves for the pressure Poisson equation using a conjugated gradient solver, which is preconditioned with a geometric multigrid algorithm. Turbulence closure is achieved through the k-ω model. The fully parallelized model uses the domain decomposition approach, making it possible to execute the code on the local supercomputer facilities.