Exploiting Superconvergence in Meshes for Optimal Representations of the Geometry with high Accuracy

Project Information

ESMORGA

Grant agreement ID: 893378

DOI

10.3030/893378

Project closed

EC signature date 26 February 2020

Start date 1 December 2020

End date 30 November 2022

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 160 932,48

EU contribution

€ 160 932,48

Coordinated by

BARCELONA SUPERCOMPUTING CENTER CENTRO NACIONAL DE SUPERCOMPUTACION
Spain

Periodic Reporting for period 1 - ESMORGA (Exploiting Superconvergence in Meshes for Optimal Representations of the Geometry with high Accuracy)

Reporting period: 2020-12-01 to 2022-11-30

Summary of the context and overall objectives of the project

The issue addressed in this project is high-fidelity simulations featuring super-accurate geometric and numerical accuracy. The project investigated tools enhancing the accuracy of large-scale simulations using unstructured high-order methods.

Super-accurate geometric and numerical accuracy are important for society because these capabilities are key to enabling high-fidelity simulation. Note that high-fidelity simulations using supercomputers play a major role in the production costs of the transport design industry: they reduce the number of full-scale tests. This reduction in the design process is key to accelerating the deployment of sustainable aircraft devices, a deployment that will be crucial to address the environmental challenge of air transportation.

The overall objectives are:
- Develop a parallel automatic mesh generation tool approximating general CAD data. This was achieved by minimizing a disparity measure that improves the accuracy compared to direct interpolation. The tool was implemented designing a Julia wrapper of the EGADS geometry kernel
- Implement the SIAC filter (MSIAC) as a standalone tool for general use exploiting superconvergence: the filter can raise the convergence order from p+1 to 2p+1. The filtered data has increased smoothness and in general, reduces the numerical error.

The main conclusions are:
- The constrained disparity optimization preserves geometric super-convergence while significantly reduce the computational times and complexity
- The solver was built on top of the EGADS kernel, enabling real-world applications such as aircraft design
- The EGADS Julia port extended the applications of the EGADS kernel to other computing languages beyond C (C++) and it is now distributed within the ESP software
- The code was parallelized and tested on distributed memory using the MareNostrum4 and revealing further computational efficiency
- The MSIAC tool was successfully implemented as a standalone tool and handles handles 2D triangular and quad unstructured meshes, and 3D structured meshes
- The filter was tested against turbulent flows from numerical solutions using FEM, DG (double Mach reflection) and including unstructured meshes (Trixie)

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Next, an overview of the work is given:

1. To enable complex CAD geometry, the curved mesher was linked with the EGADS kernel
2. To demonstrate super-convergence of the geometric approximation, a numerical study on analytic curves and CAD models were performed
3. To prove and understand geometric super-convergence, a theoretical and empirical analysis of the solution of the non-linear equations for the geometric disparity was performed
4. To verify the geometric super-convergence, a new constrained solver was fully tested on CAD models including aircraft prototypes.
5. To demonstrate super-convergence to 3D numerical solutions, the fellow developed a software tool for high-order solutions raising the convergence order through numerical filtering.

For the project main results, the following points overview their exploitation and dissemination:

Result 1. A parallel, robust, automatic curve mesh generation tool

ESMORGA Software: https://gitlab.com/Xulia/esmorga

Papers:
J. Docampo-Sánchez, E.Ruiz-Gironés, X. Roca. 2022. An efficient solver to approximate CAD curves with super-convergent rates. SIAM IMR22
J. Docampo Sánchez. 2022. Efficient parallel optimization for approximating CAD curves featuring super-convergence. Computer-Aided Design (accepted)

Scientific talks:
A specific-purpose solver to approximate planar curves with super-convergent rates. ICOSAHOM 2021
An efficient solver to approximate CAD curves with super-convergent rates. SIAM IMR22

Result 2. A filtering software package for post-processing numerical data

Homepage: https://siac-magic.gitlab.io/web/
MSIAC Software: https://gitlab.com/msiac-tool

Conferences:
1. "A filtering framework for Finite Volume/Element Schemes", High-Order NOnlinear numerical Methods for evolutionary PDEs: Theory and applications (HONOM) 2022 Spain
2. "A filtering framework for Finite Volume/Element Schemes", XVIII International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP) 2022 Spain
3. "A filtering framework for Finite Volume/Element Schemes", North American High Order Methods Conference (NAHOMCon) 2022 USA
4. Session Chair: shock capturing & filtering, North American High Order Methods Conference (NAHOMCon) 2022 USA
5. SIAM CSE23 mini-symposium co-organiser (2 sessions): Numerical Filtering and Property Preserving Methods

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The project has gone beyond the state of the art in super-convergence for geometric and numerical approximations. Regarding geometric approximations, existing curved meshers provide standard convergence to the target geometry. This project provides the first parallel curved mesher that demonstrates super-convergence. Regarding PDE solutions, SIAC filter have been only used in strucutred meshes. The MSIAC project provides a stand-alone tool for general numerical filtering.

The expected results until the end of the project are super-accurate tools for mesh generation and flow visualization of CFD simulations. The disparity-based curved mesher is a robust, automatic tool generating optimal high-order meshes with extra accuracy. This addresses a known issue in the high-order simulation community: geometric accuracy is usually lower than the required solver accuracy. Moreover, the new mesher is driven by a geometric kernel (EGADS), providing continuous geometry and direct communication between the mesh and the CAD model. The resulting open-source tool has been parallelized and integrated within EGADSlite, allowing computations on distributed memory, and becoming suitable for large-scale simulations. It can be used by any member of the scientific and industry community interested in high-order numerical simulations.

SIAC filters raise the order of accuracy and levels of continuity of Finite Element / Discontinuous Galerkin (FEM-DG) data. They have been applied for shock detection and reconstructing turbulent vorticity. Extending the SIAC filter to general 3D data provides a tool for the scientific community studying fluid flow phenomena in aeronautic and naval problems, plasma physics and renewable power. The MSIAC filtering package is a standalone open-source tool that only requires a mesh and a field file as input. It currently supports unstructured 2D data and structured 3D hexes. It has been tested against analytic fields as well as DG data computed using the Trixie package.

In perspective, the results have potential impact not only in computational engineering but also in the economy of the aeronautic industry and the societal aspect of sustainable air transport. In computational engineering, the developed tools are key to enable high-fidelity aerodynamic simulations featuring super-accurate geometric and numeric accuracy. Second, for the economy of the aeronautic industry, these high-fidelity simulations will help to perform accurate analyses of the aerodynamic performance of the next generation of sustainable air transport vehicles. Finally, for society, these sustainable aircraft designs will be crucial to addressing the environmental challenge of air transportation.

MSIAC package

Performance of the parallel constrained disparity mesher