Implementation of the Arbitrary Lagrangian-Eulerian (ALE) method in the GPU-targeting spectral element solver NekRS

Organisations involved

ETH Zurich, AUTH

Codes involved


Exascale Challenge Demonstrators involved



NekRS, an exascale ready next-generation code, is the successor of the spectral element solver Nek5000 targeting extreme-scale computing on multicore and many-core systems as well as graphics processing units. Both codes employ the spectral element method for spatial discretization to achieve high accuracy with minimal data movement while advanced algorithms, scalable iterative solvers and high-order discretizations enable the efficient simulation of non-reactive and reactive turbulent flows on leadership-class high performance computing systems.

The extension of the NekRS capabilities towards the simulation of time-varying geometries is essential for the direct numerical simulation of flow and combustion in engine and engine-like geometries on the upcoming Exascale systems. The simulations will be performed in the framework of the Center of Excellence in Combustion (CoEC), a collective effort to exploit Exascale computing technologies to address fundamental challenges related to combustion technologies and decarbonization.


In order to simulate domains with moving boundaries like those encountered in internal combustion engines, the Arbitrary Lagrangian-Eulerian (ALE) formulation was implemented in NekRS and as a first step was validated by simulating compression in the TCC-III engine.

The work was performed in a collaboration between ETH Zurich and the Center for Efficient Exascale Discretizations (CEED).


The next generation high performance computing systems will be heavily based on hardware accelerators like GPUs to reach Exascale performance. The development of new software geared towards these systems is necessary to harness efficiently the three orders of magnitude increase in computational power in order to enable fundamental insights into the complex multi-scale and multi-physics phenomena encountered in combustion devices and support the decarbonization goals of the European Union in the Energy and Transportation sectors.

Temperature stratification on a 2-D slice through the cylinder axis
of the TCC-III engine at different crank angle degrees (CAD) during
compression (bottom dead center at 180 CAD)