Exact Representation of Curved Material Interfaces and Boundaries in High-Order Finite Element Simulations

Project Overview

The goal of this project was to improve the accuracy of numerical simulations around material interfaces and boundaries, in the context of finite element (FE) discretizations. It aimed to provide a solution for the long-standing issues of (i) artificial mixing of materials in multiphysics simulations and (ii) the need for precise geometric body-fitted mesh generation for complex topologies. At the same time, the newly developed algorithms were designed to maintain all the benefits of the high-order FE methods, namely, computational efficiency, high-order accuracy, and generality with respect to space dimension and order of the discretization. The resulting algorithms benefit simulations with improved fidelity; fast, reliable, and simple model/mesh preparation procedures; and scalable solvers ready for the next generation exascale architectures.

The technical approach is based on combining the recently developed shifted boundary/interface methods (SBIM) with high-order FE discretizations of practical problems of interest to Lawrence Livermore National Laboratory (LLNL). The SBIM is an immersed grid technique that avoids geometric operations for resolving cut elements by constructing a surrogate (shifted) interface with controllable accuracy. The projected developed new theory and methods approaches for numerical simulations of compressible shock hydrodynamics and shape/topology optimization. The results of these methods indicate that the SBIM approach can lead to better resolution around material interfaces and domain boundaries in practical problems at LLNL. 

Mission Impact

The project develops predictive simulation tools and capabilities to meet future national security challenges. The development targets two codes of significant importance to Lawrence Livermore National Laboratory (LLNL) : a compressible shock hydrodynamics next-gen production code, and the Livermore Design Optimization code (LiDO). In both codes the accurate resolution of material interfaces and complex boundaries is essential. It is envisioned that the ability to solve multiple physics accurately without any geometric operations opens an enormous number of possibilities for advancing LLNL capabilities in multiple mission areas.

Publications, Presentations, and Patents

Gomez-Lozada, Felipe, Carlos Andres del Valle, Julian David Jimenez-Pez, Boyan Lazarov, and Juan Galvis. 2023. "Modeling Simulation of Brinicle Formation." Royal Society Open Science (in press). LLNL-JRNL-844371.

M. Nabil Atallah,"The High-Order Shifted Boundary Method for Finite Element Hydrodynamics" (Presentation, 17th US National Congress on Computational Mechanics, Albuquerque, NM, 2023). LLNL-PRES-851838.

M. Nabil Atallah, "The High-Order Shifted Boundary Method" (Presentation, 22nd Computational Fluids Conference, Cannes, France, 2023). LLNL-PRES-847873.

Atallah, Nabil M.,"Exact Representation of Curved Material Boundaries and Interfaces in High-Order Finite Element Simulations" (Presentation, 15th World Congress on Computation Mechanics & 8th Asian Pacific Congress on Computation Mechanics, Yokohama, Japan, 2022). LLNL-PRES-837357.

Boyon Lazarov,"Topology and Shape Optimization Based on the Shifted Boundary Method" (Presentation, Engineering Mechanics Institute Conference, Baltimore, MD, 2022). LLNL-PRES-835768.

M. Nabil Atallah, "The Shifted Boundary Method: A Framework for Immersed Computational Mechanics" (Presentation, Engineering Mechanics Institute Conference, Baltimore, MD, 2022). LLNL-PRES-835715.