An octree structured finite volume based solver

Abstract

The present work describes the development of a parallel distributed-memory implementation, of an octree data structure, linked to an adaptive cartesian mesh to solve the Navier–Stokes equations. The finite volume method was used in the spatial discretization where the advective and diffusive terms were approximated by the central differences method. The temporal discretization was accomplished using the Adams–Bashforth method. The velocity-pressure coupling is done using the fractional-step method of two steps. Moreover, all simulated results were obtained using a external solver for the Poisson equation, from the pressure correction, in the fractional step method. Results are presented both for adaptive octree mesh and for a mesh without refinement. These were determined in the verification and validation processes for the present computational code. Finally, we consider the simulations for the problems of a laminar jet and the lid-driven cavity flow. Numerical results are compared with numerical and experimental data.