Development of a scalable finite element solution to the Navier – Stokes equations. (English) Zbl 1038.76524

Summary: A scalable numerical model to solve the unsteady incompressible Navier-Stokes equations is developed using the Galerkin finite element method. The coupled equations are decoupled by the fractional-step method and the systems of equations are inverted by the Krylov subspace iterations. The data structure makes use of a domain decomposition of which each processor stores the parameters in its subdomain, while the linear equations solvers and matrices constructions are parallelized by a data parallel approach. The accuracy of the model is tested by modeling laminar flow inside a two-dimensional square lid-driven cavity for Reynolds numbers at \(1,000\) as well as three-dimensional turbulent plane and wavy Couette flow and heat transfer at high Reynolds numbers. The parallel performance of the code is assessed by measuring the CPU time taken on an IBM SP2 supercomputer. The speed up factor and parallel efficiency show a satisfactory computational performance.


76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65Y05 Parallel numerical computation


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