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Computational fluid dynamics on wildly heterogeneous systems
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In the last decade, high-order methods have gained increasedattention. These combine the convergence properties ofspectral methods with the geo-metrical flexibility of low-ordermethods. With restrictive time steps, implicit treatment ofdiffusion and pressure terms is mandatory. Therefore, efficientsolution of elliptic equations is of central importance for fastflow solvers. As the operators scale with O(p · nDOF), where nDOFis the number of degrees of freedom and p the polynomialdegree, the runtime of the best available multigrid algorithmsscales with O(p · nDOF) as well. This super-linear scalinglimits the applicability of high-order methods to mid-rangepolynomial orders, constituting a major road block towardsfaster flow solvers.This work reduces the super-linear scaling of elliptic solvers toa linear one. The devised methods are combined into a flowsolver, which preserves this linear scaling. Furthermore, amultigrid method reduces the cost of implicit treatment of thepressure to the one for explicit treatment of the convectionterms. Lastly, benchmarks confirm that the solver outperformsestablished high-order codes.
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