Development of a finite element flow solver for solving three-dimensional incompressible Navier–Stokes solutions on multiple GPU cards

•A LBB-based upwinding Petrov–Galerkin FE model is proposed.•An effective strategy is employed to get the convergent solution.•An effective EBE-based matrix-vector product kernel is implemented on multi-GPUs.•The large-sized problem can be solved and the computing time is largely reduced. In this paper a multi-GPU-based finite element flow solver is developed to solve the three-dimensional incompressible Navier–Stokes equations at steady-state. To circumvent the convective instability problem at high Reynolds numbers, the proposed streamline upwinding finite element model minimizes the wavenumber error for the convection terms. Mixed finite element formulation is adopted and the resulting nearly ill-conditioned finite element equations are solved iteratively. To avoid the Lanczos or pivoting breakdown, the finite element equations are first normalized. The computationally efficient preconditioned conjugate gradient (PCG) solver can then be applied to get the unconditionally convergent solution. The developed finite element code implemented on multi-GPU cards will be verified and validated by solving the problem amenable to analytical solution and the benchmark lid-driven cavity problem, respectively.