Parallel Algorithms for Complex Flows

Rüde U (2018)

Publication Type: Conference contribution, Conference Contribution

Publication year: 2018

This talk will report about recent progress to simulate complex ﬂow prob-

lems using ﬁnite element methods or advanced kinetic methods, highlighting

their di↵erences and advantages when implemented on modern supercom-

puter systems.

The ﬁnite element method for incompressible ﬂows often requires the

solution of systems with saddle point structure. We will present our ex-

perience with a parallel multigrid algorithm using hierarchical hybrid grids

[1]. For a geophysical application, the simulation of Earth Mantle convec-

tion, we will demonstrate that the solution of FE systems with in excess of

1012 degrees of freedom is feasible on current petascale class supercomputers

[4]. The highest eﬃciency is achieved for novel matrix-free techniques where

the sti↵ness matrix is not stored but recomputed using suitably constructed

approximations in every step of the iterative multigrid solver [8].

Kinetic schemes, such as the Lattice Boltzmann method (LBM) are

structurally di↵erent since they are explicit time stepping schemes. Though

this poses time step restrictions, these methods can often beneﬁt from being

parallelizable with only nearest neighbor communication [2]. Du to their

structural simplicity, LBM methods are sometimes also more ﬂexible and

more extensible [6]. One particular strength of the LBM is the simulation

of suspensions [5, 3] and multiphase ﬂows via a direct numerical simulation,

i.e. when each particle, droplet, or bubble, are fully resolved. As one ex-

ample we will present e↵orts to simulate the sediment transport in a river

bed with fully resolved and geometrically modeled grains. Here we rely

on the LBM methods realized in the waLberla framework [2] that exhibit

not only excellent scalability, but that are also carefully optimized using