Parallel smoothing pressure correction solver for biomedical flow problems: convergence criteria, preconditioning, scalability

Kathrin Burckhardt, Dominik Szczerba, Esra Neufeld, Krishnamurthy Muralidhar, and Niels Kuster, Progress in Computational Fluid Dynamics, Volume 16, Issue 4, pp. 201–215, online August 10, 2016

A fast, parallel flow solver based on a pressure-correction approach is analysed. It is especially suitable for biomedical flow problems due to the use of unstructured meshes and the ability to tackle large problems. The original smoothing pressure correction method was enhanced by parallelisation, efficient linear solvers, and the introduction of a generic linear stopping criterion. The solver was verified and its accuracy demonstrated by means of a range reference benchmarks, and its applicability to biomedical problems was demonstrated by simulating transient blood flow in the human aortic bifurcation. Scalability was investigated on a Cray XT5. High parallel efficiency could be achieved when solving the momentum equations with scalable low-cost preconditioning. Computationally more expensive multigrid preconditioning proved to be advantageous when solving the pressure correction equation, but restricted scalability to a range of up to 30 computing cores.

The scientific and technical impact of the study can be summarized as:

  • A novel, highly parallelizable variant of the smoothing pressure-correction approach was robustly implemented
  • The method was verified, and its applicability to relevant biomedical flow problems was demonstrated
  • Adequate preconditioning significantly reduces the run time, and preconditioners that are economical in terms of computation and communication costs are suitable for the momentum equation system
  • Low-cost preconditioning allows scalability up to hundreds of computing cores
  • The bottleneck is the pressure correction equation, which can be efficiently overcome with computationally expensive algebraic multigrid techniques
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