Development of a two-dimensional Navier-Stokes solver for laminar flows using cartesian grids

Şahin, Mehmet Serkan
A fully automated Cartesian/Quad grid generator and laminar flow solver have been developed for external flows by using C++. After defining the input geometry by nodal points, adaptively refined Cartesian grids are generated automatically. Quadtree data structure is used in order to connect the Cartesian cells to each other. In order to simulate viscous flows, body-fitted quad cells can be generated optionally. Connectivity is provided by cut and split cells such that the intersection points of Cartesian cells are used as the corners of quads at the outmost row. Geometry based adaptation methods for cut, split cells and highly curved regions are applied to the uniform mesh generated around the geometry. After obtaining a sufficient resolution in the domain, the solution is achieved with cellcentered approach by using multistage time stepping scheme. Solution based grid adaptations are carried out during the execution of the program in order to refine the regions with high gradients and obtain sufficient resolution in these regions. Moreover, multigrid technique is implemented to accelerate the convergence time significantly. Some tests are performed in order to verify and validate the accuracy and efficiency of the code for inviscid and laminar flows.