Asynchronous exascale PDE solvers: exploiting extreme parallelism for turbulence simulations

Future exascale computing systems will be available to study

multi-physics multi-scale natural phenomena and engineering systems.

Many of these can be described by partial differential equations (PDEs)

that may be tightly coupled with long-range correlations. A prime example

is high-Reynolds number turbulence

which is critical in phenomena as diverse as mixing in an engine, pollutants in

the atmosphere, aerodynamic drag, and the structure of the observable universe.

Because of the exceedingly complex nature of the governing equations,

little is known from its analytical treatment and most advances

have relied on numerical simulations.

The relentless increase in computational power

has enabled simulations at more realistic conditions opening the door

to important scientific breakthroughs.

This explosion in computational power has been realized through massive

parallelism. Current simulation approaches present significant challenges

with the extreme levels of parallelisms expected on exascale systems,

In this talk we first discuss these computational

challenges in current approaches and introduce a novel concept

for simulations which exploits relaxed synchronizations between processing elements.

We show how this approach can effectively mitigate

(or eliminate) synchronization and communication overheads

which are well-known bottlenecks expected at exascale.

We will show how new errors emerge because of asynchrony and how

new numerical schemes can be designed to retain high accuracy.

These schemes are found to be able to accurately capture turbulence

in realistic simulations and extend the scalability of codes

significantly. We will show results from simple model problems,

to compressible turbulence and detonations.

We will conclude with a perspective on the new opportunities

presented by asynchronous schemes at exascale and future work needed.