Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

We discuss aspects of implementation and performance of parallel iterative solution techniques applied to low Reynolds number flows around fixed and moving rigid bodies. The incompressible Navier-Stokes equations are discretised with Taylor-Hood finite elements in combination with a semi-implicit pressure-correction method. The resulting sequence of convection-diffusion and Poisson equations are solved with preconditioned Krylov subspace methods. To achieve overall scalability we consider new auxiliary algorithms for mesh handling and assembly of the system matrices. We compute the flow around a translating plate and a rotating insect wing to establish the scaling properties of the developed solver. The largest meshes have up to 132 × 10^6 hexahedral finite elements leading to around 3.3 × 10^9 unknowns. For the scalability runs the maximum core count is around 65.5 × 10^3. We find that almost perfect scaling can be achieved with a suitable Krylov subspace iterative method, like conjugate gradients or GMRES, and a block Jacobi preconditioner with incomplete LU factorisation as a subdomain solver. In addition to parallel performance data, we provide new highly-resolved computations of flow around a rotating insect wing and examine its vortex structure and aerodynamic loading.This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) through grant # EP/G008531/1. Additional support was provided by the Czech Science Foundation through grant 14-02067S, and by the Czech Academy of Sciences through RVO:67985840. The presented computations were performed on HECToR at the Edinburgh Parallel Computing Centre through PRACE-2IP (FP7 RI-283493).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.compfluid.2015.08.02

Parallel implementation of Multilevel BDDC

In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method.Comment: 9 pages, 2 figures, 3 table

Aplikace apriorních odhadů chyby pro metodu konečných prvků pro zjemnění sítě poblíž singularity v proudění vazké nestlačitelné tekutiny

In the paper we describe application of apriori error estimates for generation of finite element mesh near singularity for accurate solution of the Navier-Stokes equations

Solution of incompressible flow using FEM adjusted to singularity

We describe solution of incompressible fluid flow using the finite element method on meshes adjusted to singularity

Combining adaptive mesh refinement with a parallel multilevel BDDC solver

This research was supported by the Czech Science Foundation through grant 1809628S, and by the Czech Academy of Sciences through RVO:67985840. Computational time on the Salomon supercomputer has been provided by the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme, as well as Czech Ministry of Education, Youth and Sports via the project Large Research, Development and Innovations Infrastructures (LM2011033).Adaptive mesh refinement and domain decomposition. Adaptive mesh refinement is an important part of solving problems with complicated solutions or when a prescribed accuracy needs to be achieved. In this approach, solution is found on a given mesh and its local error is estimated. Regions where the estimated error is high are then refined to improve the accuracy, and the solution is recomputed. This strategy leads to accumulation of degrees of freedom to regions with abrupt changes in the solution, such as boundary or internal layers

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

We discuss aspects of implementation and performance of parallel iterative solution techniques applied to low Reynolds number flows around fixed and moving rigid bodies. The incompressible Navier-Stokes equations are discretised with Taylor-Hood finite elements in combination with a semi-implicit pressure-correction method. The resulting sequence of convection-diffusion and Poisson equations are solved with preconditioned Krylov subspace methods. To achieve overall scalability we consider new auxiliary algorithms for mesh handling and assembly of the system matrices. We compute the flow around a translating plate and a rotating insect wing to establish the scaling properties of the developed solver. The largest meshes have up to 132 × 106 hexahedral finite elements leading to around 3.3 × 109 unknowns. For the scalability runs the maximum core count is around 65.5 × 103. We find that almost perfect scaling can be achieved with a suitable Krylov subspace iterative method, like conjugate gradients or GMRES, and a block Jacobi preconditioner with incomplete LU factorisation as a subdomain solver. In addition to parallel performance data, we provide new highly-resolved computations of flow around a rotating insect wing and examine its vortex structure and aerodynamic loading