Discrete embedded boundary method with smooth dependence on the evolution of a fluid‐structure interface

Abstract

Embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid-structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody-fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi-discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interface Γ F∕S h . This hinders their application to the gradient-based solution of fluid-structure optimization problems. Discrete events also promote spurious oscillations in the post-processing of time-dependent results computed at Γ F∕S h .z This paper addresses these issues in the context of Finite Volume method with Exact two-material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi-discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed on Γ F∕S h . Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions of Γ F∕S h .

A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling

“…Due to the anticipated large shape and topology changes of the flexible parachute system during its deployment, and the unrestrained motion of the rigid forebody, the FSI simulation of supersonic PID is performed using the arbitrary Lagrangian–Eulerian (ALE) formulation of the embedded (or immersed) boundary method FIVER (finite volume method with exact two‐material Riemann problems) 39 described in Reference 40. Hence, the parachute system and the forebody are embedded in a background CFD grid that is adapted in time to resolve all flow features of interest (boundary layers, shocks, and wakes) using automatic adaptive mesh refinement (AMR) 41 .…”

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

“…38,39 However, as for data-based calibration, EBMs and IBMs might not be favorable, because they are generally not differentiable and the quantities of interest, like surface stresses and forces, require special treatments to retain smoothness. 25,[40][41][42][43] The non-differentiation and lack of smoothness are rooted in the enforcement of fluid-structure interface conditions on a non-interface-conforming mesh. More specifically, the stencils, which are used to evaluate discrete delta function or reconstruct fluid states at the "sharp interface," keep changing along with the moving interface.…”

“…There are variants under other names, including cut cell methods, 29‐31 fictitious domain methods, 32‐36 ghost fluid‐structure methods, 37 and immersed boundary‐Lattice Boltzmann methods 38,39 . However, as for data‐based calibration, EBMs and IBMs might not be favorable, because they are generally not differentiable and the quantities of interest, like surface stresses and forces, require special treatments to retain smoothness 25,40‐43 . The non‐differentiation and lack of smoothness are rooted in the enforcement of fluid‐structure interface conditions on a non‐interface‐conforming mesh.…”

Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework

“…There are variants under other names, including cut cell methods 29,30,31 , fictitious domain methods 32,33,34,35,36 , ghost fluid-structure methods 37 , and immersed boundary-Lattice Boltzmann methods 38,39 . However, as for data-based calibration, EBMs and IBMs might not be favorable, because they are generally not differentiable and the quantities of interest, like surface stresses and forces, require special treatments to retain smoothness 25,40,41,42,43 . The non-differentiation and lack of smoothness are rooted in the enforcement of fluid-structure interface conditions on a non-interface-conforming mesh.…”