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Adaptive Immersed Mesh Method (AIMM) for Fluid Structure Interaction

R. Nemer, A. Larcher, E. Hachem

TL;DR

The paper introduces the Adaptive Immersed Mesh Method (AIMM), a hybrid Fluid-Structure Interaction framework that couples a Lagrangian solid solver with an Eulerian fluid solver by immersing the solid in a shared fluid–solid mesh and tracking the interface via a level-set function. Both solvers are stabilized with Variational Multi-Scale (VMS) methods to enable first-order unstructured elements while maintaining stability, and anisotropic mesh adaptation concentrates refinement along the interface using an edge-based error estimator and gradient recovery. The AIMM coupling enforces two-way velocity and stress continuity at the FSI interface and leverages a moving mesh approach to accurately resolve boundary layers and contact surfaces. The method is validated on 2D benchmarks and demonstrated on 3D FSI problems (pillar and flap configurations), showing good agreement with literature and experimental data, and highlighting its potential for robust, scalable FSI in complex, slender structures.

Abstract

Our paper proposes an innovative approach for modeling Fluid-Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration, the solid mesh is immersed within a fluid-solid mesh, all while maintaining its independent Lagrangian hyperelastic solver. The Eulerian mesh encompasses both the fluid and solid components and accommodates various physical phenomena. We enhance the interaction between solid and fluid through anisotropic mesh adaptation and the Level-Set methods. This enables a more accurate representation of their interaction. Together, these components constitute the Adaptive Immersed Mesh Method (AIMM). For both solvers, we utilize the Variational Multi-Scale (VMS) method, mitigating potential spurious oscillations common with piecewise linear tetrahedral elements. The framework operates in 3D with parallel computing capabilities. Our methods accuracy, robustness, and capabilities are assessed through a series of 2D numerical problems. Furthermore, we present various three-dimensional test cases and compare their results to experimental data.

Adaptive Immersed Mesh Method (AIMM) for Fluid Structure Interaction

TL;DR

The paper introduces the Adaptive Immersed Mesh Method (AIMM), a hybrid Fluid-Structure Interaction framework that couples a Lagrangian solid solver with an Eulerian fluid solver by immersing the solid in a shared fluid–solid mesh and tracking the interface via a level-set function. Both solvers are stabilized with Variational Multi-Scale (VMS) methods to enable first-order unstructured elements while maintaining stability, and anisotropic mesh adaptation concentrates refinement along the interface using an edge-based error estimator and gradient recovery. The AIMM coupling enforces two-way velocity and stress continuity at the FSI interface and leverages a moving mesh approach to accurately resolve boundary layers and contact surfaces. The method is validated on 2D benchmarks and demonstrated on 3D FSI problems (pillar and flap configurations), showing good agreement with literature and experimental data, and highlighting its potential for robust, scalable FSI in complex, slender structures.

Abstract

Our paper proposes an innovative approach for modeling Fluid-Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration, the solid mesh is immersed within a fluid-solid mesh, all while maintaining its independent Lagrangian hyperelastic solver. The Eulerian mesh encompasses both the fluid and solid components and accommodates various physical phenomena. We enhance the interaction between solid and fluid through anisotropic mesh adaptation and the Level-Set methods. This enables a more accurate representation of their interaction. Together, these components constitute the Adaptive Immersed Mesh Method (AIMM). For both solvers, we utilize the Variational Multi-Scale (VMS) method, mitigating potential spurious oscillations common with piecewise linear tetrahedral elements. The framework operates in 3D with parallel computing capabilities. Our methods accuracy, robustness, and capabilities are assessed through a series of 2D numerical problems. Furthermore, we present various three-dimensional test cases and compare their results to experimental data.
Paper Structure (22 sections, 71 equations, 50 figures, 6 tables)

This paper contains 22 sections, 71 equations, 50 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Solid solver
  3. Lagrangian Solid Dynamics and Hyperelastic Model
  4. Variational Multi Scale stabilization
  5. Fluid solver
  6. Newtonian incompressible equations
  7. Variational Multi Scale (VMS) stabilization
  8. Coupling
  9. Level set approach
  10. Physical continuity
  11. Edge-based mesh adaptation
  12. Edge-based error estimation
  13. Gradient recovery procedure
  14. Metric construction
  15. Numerical Validation
  16. ...and 7 more sections

Figures (50)

  • Figure 1: Different approaches for FSI.
  • Figure 2: Different approaches for FSI.
  • Figure 3: The signed distance function $\alpha$ example of an immersed circle.
  • Figure 4: Two way coupling loop.
  • Figure 5: Patch associated with node $x^i$
  • ...and 45 more figures