Computational fluid dynamics on wildly heterogeneous systems

In the last decade, high-order methods have gained increased
attention. These combine the convergence properties of
spectral methods with the geo-metrical flexibility of low-order
methods. With restrictive time steps, implicit treatment of
diffusion and pressure terms is mandatory. Therefore, efficient
solution of elliptic equations is of central importance for fast
flow solvers. As the operators scale with O(p · nDOF), where nDOF
is the number of degrees of freedom and p the polynomial
degree, the runtime of the best available multigrid algorithms
scales with O(p · nDOF) as well. This super-linear scaling
limits the applicability of high-order methods to mid-range
polynomial orders, constituting a major road block towards
faster flow solvers.
This work reduces the super-linear scaling of elliptic solvers to
a linear one. The devised methods are combined into a flow
solver, which preserves this linear scaling. Furthermore, a
multigrid method reduces the cost of implicit treatment of the
pressure to the one for explicit treatment of the convection
terms. Lastly, benchmarks confirm that the solver outperforms
established high-order codes.