Improving the efficiency of the sub-stepping velocity splitting scheme within the Nektar++ framework
File(s)
Published version
Author(s)
Type
Conference Paper
Abstract
In this work, the computational performance of the Nektar++ framework for solving the incompressible Navier-Stokes (NS) equations using Spectral h/p elements is assessed
and improved for industry-relevant geometries at high Reynolds numbers. There is an increasing need for simulating complex geometries with greater accuracy at a reduced computational cost. These simulations involve multiple spatial/temporal scales, and they should model or resolve complex transient phenomena such as turbulence transition, separation, and vortex system evolution. Standard explicit techniques require very low time steps, which are not feasible within an industrial environment, hence the need for efficient implicit time-stepping techniques. This
study uses the implicit Sub-Stepping Velocity Splitting Scheme to solve the incompressible NS equations numerically in a segregated manner. This method is distinguished by its use of a mixed discretization scheme. Specifically, it employs Discontinuous Galerkin discretization to solve an unsteady advection equation during the Advection step while using Continuous Galerkin discretization for the Pressure and Diffusion steps. First, the performance of the proposed method is evaluated in terms of its numerical efficiency for both serial and parallel computations. Then, the Advection, Pressure, and Diffusion steps are explored based on the fundamental kernel
efficiency to identify the most time-consuming components, aiming at reducing the memory footprint and moving them closer to the CPU-bound of the roofline model. We will present a systematic performance analysis, the challenges, and the advancements for mixed discretization time-stepping techniques relevant to any available Finite Element code aiming at solving exascale industrial problems.
and improved for industry-relevant geometries at high Reynolds numbers. There is an increasing need for simulating complex geometries with greater accuracy at a reduced computational cost. These simulations involve multiple spatial/temporal scales, and they should model or resolve complex transient phenomena such as turbulence transition, separation, and vortex system evolution. Standard explicit techniques require very low time steps, which are not feasible within an industrial environment, hence the need for efficient implicit time-stepping techniques. This
study uses the implicit Sub-Stepping Velocity Splitting Scheme to solve the incompressible NS equations numerically in a segregated manner. This method is distinguished by its use of a mixed discretization scheme. Specifically, it employs Discontinuous Galerkin discretization to solve an unsteady advection equation during the Advection step while using Continuous Galerkin discretization for the Pressure and Diffusion steps. First, the performance of the proposed method is evaluated in terms of its numerical efficiency for both serial and parallel computations. Then, the Advection, Pressure, and Diffusion steps are explored based on the fundamental kernel
efficiency to identify the most time-consuming components, aiming at reducing the memory footprint and moving them closer to the CPU-bound of the roofline model. We will present a systematic performance analysis, the challenges, and the advancements for mixed discretization time-stepping techniques relevant to any available Finite Element code aiming at solving exascale industrial problems.
Date Issued
2024-10-29
Date Acceptance
2024-10-29
Citation
ECCOMAS 2024, 2024
Publisher
Scipedia, SL.
Journal / Book Title
ECCOMAS 2024
Copyright Statement
© 2024 The Author(s). Published by Scipedia, SL. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (https://creativecommons.org/licenses/by-nc-sa/4.0/).
Source
9th European Congress on Computational Methods in Applied Sciences and Engineering
Publication Status
Published
Start Date
2024-06-03
Finish Date
2024-06-07
Coverage Spatial
Libson, Portugal
Date Publish Online
2024-10-29