Success Story: High-fidelity simulation using Adaptive Mesh Refinement with Spectral Element Method solver

Success story # Highlights:

Keywords:

HPC
CFD
High fidelity simulations
Spectral element method
Adaptive mesh refinement

Industry sector: Automotive, Aerospace
Key codes used: Neko, Nek5000

benefits for further research:

Control of computational error at optimal computational cost
Reduced mesh size resulting in reduced computational cost
Simplified meshing and possibility to model flow cases with unknown dynamics

Organisations & Codes Involved:

KTH is a leading Scandinavian research centre and the largest technical university in Sweden. It conducts research and education in engineering and technology, collaborating with prominent partners worldwide and participating in a variety of key projects.

Neko

Nek5000

SCIENTIFIC CHALLENGE:

High-fidelity modelling of turbulent flows with high Reynolds numbers is challenging due to the wide range of the flow features that have to be resolved. This makes running simulations computationally expensive and poses a meshing problem, as the flow dynamics may not be a priori known. A common solution is to use turbulence modelling that lowers resolution requirements and thus reduces computational costs. However, this introduces modelling errors, making simulations of flows with complex dynamics less reliable. It is important to be able to perform high accuracy simulations of these complex flows since they could be used to develop new turbulence models.

Solution:

We are implementing an Adaptive Mesh Refinement workflow in Neko’s CFD solver that would allow for modifying the computational grid during runtime. For this purpose, we use native to the Spectral Element Method (SEM) decomposition of the domain into non-overlapping spectral subdomains called elements, and we perform recursive splitting/merging of these elements to create new ones. The resulting mesh is complex and requires special treatment of the nonconforming interfaces, but allows one to complete the simulation at minimal cost, as higher resolution is placed only where needed.
The whole process can be based on the estimated computational error, increasing the robustness and reliability of the solution. An important aspect here is its efficient use of the computing resources.

SCIENTIFIC IMPACT OF THIS RESULT:

AMR is a required feature of a CFD solver, enabling control of the computational error at optimal computational cost. It enables modelling flow cases with unknown dynamics, as the specific flow features can be captured through dynamic adjustment of the mesh during runtime. At the same time, meshing at the pre-processing step gets simplified and more generic grids can be created.

In addition, various tools and algorithms may need a simple method to increase local grid resolution, making AMR a useful solver component. An example could be an immersed boundary method that provides a great deal of flexibility in modelling flows in complex geometric configurations without tedious meshing, but this requires
sufficient resolution to mimic an object’s surface.

The significant reduction in computational cost and increased solution reliability will let researchers run bigger and more complex cases of industrial relevance. A good example is high-fidelity simulation of a drone rotor, which would give more insight into
its flow dynamics and noise generation.

Potential EXCELLERAT Services:

1) Adaptive Mesh Refinement (AMR) Integration: by adjusting the mesh based on the solution’s needs, this significantly reduces computational cost while ensuring high accuracy in regions where it’s most needed. The value is the efficient error control at optimal cost.

2) Immersed Boundary Method (IBM) for Complex Geometries: it allows for efficient simulation of flows around complex objects, such as drone rotors, without the need for detailed meshing of the geometry. This is especially important for complex industrial applications, as it simplifies the meshing process and ensures that important flow features near object surfaces are identified. The value is the simplified geometric modeling with flexibility in Complex Flows.

3) Load Balancing for Parallel Computation: it optimizes parallel computing resources, ensuring that AMR simulations can efficiently use multi-core or distributed computing environments to speed up the solution process. The value is the efficient use of computational resources at scale.

time period:

Adaptive Mesh Refinement (AMR) runs of the use case performed with AMR version of Nek5000 are ongoing and the first results should be ready in the middle of 2025.

The CPU version of AMR Neko is expected to be ready at the end of 2025 and a GPU version will be developed in 2026.