Implementation of a parallel ADI algorithm on a finite volume GPU-based elementary porous media flow computation

Abstract

In this work we present flow simulations in laminar and turbulent regime within a representative elementary volume of a simplified porous media by solving the Navier–Stokes equations and a Low-Re turbulence $$k{-}\epsilon$$ model. Numerical solution was achieved with an implementation of the SIMPLE algorithm for pressure velocity coupling of variables, and the solution of the tridiagonal systems of algebraic equations was accomplished by a parallelized ADI scheme based on the Thomas algorithm. Implementation of the numerical solution was done with an in-house C code which combined OMP and CUDA technologies for computations based on CPU and GPU, respectively. Exponential structured grids were employed in the wall vicinity to capture the turbulence behavior. Results indicate that similar profiles for velocity, pressure, turbulent kinetic energy and its dissipation were found. Several CUDA grids were tested and their performances measured over two GPUs: GTX 680 and GTX TITAN. Considerable speedup was achieved by the GPUs over the CPU schemes even without the use of the device shared memory which was not explored due to the nature of the algorithm.